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mathematical finite group theory, the concept of regular p-group captures some of the more important properties of abelian p-groups, but is general enough
Regular_p-group
Group in which the order of every element is a power of p
specifically group theory, given a prime number p, a p-group is a group in which the order of every element is a power of p. That is, for each element g of a p-group
P-group
Topics referred to by the same term
morphisms Regular numbers, numbers which evenly divide a power of 60 Regular p-group, a concept capturing some of the more important properties of abelian p-groups
Regular
Sequence of characters that forms a search pattern
meaning "Global search for Regular Expression and Print matching lines"). Around the same time that Thompson developed QED, a group of researchers including
Regular_expression
Spanish Army unit
The Fuerzas Regulares Indígenas ("Indigenous Regular Forces"), known simply as the Regulares (Regulars), are infantry units of the Spanish Army, largely
Regulares
Finite-state machine in automata theory
is p-regular (also: a pure-group language) if it is accepted by a permutation automaton. For example, the set of strings of even length forms a p-regular
Permutation_automaton
Concept in mathematics
class of finite p-groups whose structure was sufficiently similar to that of finite abelian p-groups, the so-called, regular p-groups. The relationship
Omega_and_agemo_subgroup
Danish shipping and logistics company
Information". A. P. Moller - Maersk Group A/S. Archived from the original on 8 February 2013. Retrieved 10 January 2013. "Maersk Line - About Us". A. P. Møller
Maersk
Solid with twenty equal triangular faces
The regular icosahedron (or simply icosahedron) is a convex polyhedron that can be constructed from a pentagonal antiprism by attaching two pentagonal
Regular_icosahedron
Solid with 12 equal pentagonal faces
A regular dodecahedron or pentagonal dodecahedron is a dodecahedron (a polyhedron with 12 faces) composed of regular pentagonal faces, three meeting at
Regular_dodecahedron
Locally compact topological group with an invariant averaging operation
version is that the support of the regular representation is the whole space of irreducible representations. In discrete group theory, where G has the discrete
Amenable_group
Any of the five regular polyhedra
geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent
Platonic_solid
Solid with four equal triangular faces
A regular tetrahedron is a polyhedron with four equilateral triangular faces. A regular tetrahedron is a tetrahedron (that is, a four-sided polyhedron)
Regular_tetrahedron
Representation theory of groups
particular the theory of group representations, the regular representation of a group G is the linear representation afforded by the group action of G on itself
Regular_representation
( p 3 , p ) {\displaystyle (p^{3},p)} , ( p 2 , p 2 ) {\displaystyle (p^{2},p^{2})} , ( p 2 , p , p ) {\displaystyle (p^{2},p,p)} , ( p , p , p , p )
Descendant tree (group theory)
Descendant_tree_(group_theory)
{\displaystyle p^{k}} powers is again a p k {\displaystyle p^{k}} th power. Regular p-groups are an example of power closed groups. On the other hand, powerful p-groups
Power_closed
Solid with eight equal triangular faces
Thinking. Macmillan Publishing. p. 183. ISBN 978-0-02-065320-2. Coxeter 1973, p. 130, §7.6 The symmetry group of the general regular polytope; "simplicial subdivision"
Regular_octahedron
Term in abstract algebra
order p. The latter question has positive answer whenever G has one of the following conditions: G is nilpotent of class 2 G is a regular p-group G / Z(G)
Inner_automorphism
Gamma matrices for arbitrary Clifford algebras
gamma group is finite, and has at most 2 p + q + 2 {\displaystyle 2^{p+q+2}} elements in it. The gamma group is a 2-group but not a regular p-group. The
Higher-dimensional gamma matrices
Higher-dimensional_gamma_matrices
These characters appear in the American animated television series Regular Show, created by J. G. Quintel for Cartoon Network. The series revolves around
List of Regular Show characters
List_of_Regular_Show_characters
Equiangular and equilateral polygon
where each distinct p i {\displaystyle p_{i}} is a Pierpont prime. The symmetry group of an n-sided regular polygon is the dihedral group Dn (of order 2n):
Regular_polygon
Polytope with highest degree of symmetry
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. In
Regular_polytope
Shape with six sides
symmetries express nine distinct symmetries of a regular hexagon. John Conway labels these by a letter and group order. r12 is full symmetry, and a1 is no symmetry
Hexagon
Standings and Results for Group A of the Regular Season phase of the FIBA European Championship 1992–93 basketball tournament. Main page: FIBA European
1992–93 FIBA European Championship Regular Season Group A
1992–93_FIBA_European_Championship_Regular_Season_Group_A
Roman Catholic priests living in community under a religious rule
monasteries of monks. All canons regular are to be distinguished from secular canons who belong to a resident group of priests but who do not take public
Canon_regular
In mathematics, a regular element of a Lie algebra or Lie group is an element whose centralizer has dimension as small as possible. For example, in a
Regular element of a Lie algebra
Regular_element_of_a_Lie_algebra
Polyhedron with regular congruent polygons as faces
A regular polyhedron is a polyhedron with regular and congruent polygons as faces. Its symmetry group acts transitively on its flags. A regular polyhedron
Regular_polyhedron
Four-dimensional analogues of the regular polyhedra in three dimensions
mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular polyhedra
Regular_4-polytope
Mathematical category with finite limits and coequalizers
Carsten (1998). "Regular Categories and Regular Logic". BRICS Lectures Series LS-98-2. Pedicchio & Tholen 2004, p. 169 Pedicchio & Tholen 2004, p. 179 Barr,
Regular_category
completely regular inverse semigroup. In a completely regular semigroup, each Green H-class is a group and the semigroup is the union of these groups. Hence
Completely_regular_semigroup
American political faction formed for the 1944 presidential election
The Texas Regulars was a group based in Texas which was formed in 1944 to deny Franklin D. Roosevelt a majority of the Electoral College in the 1944 presidential
Texas_Regulars
geometry, a regular scheme is a locally Noetherian scheme whose local rings are regular everywhere. Every smooth scheme is regular, and every regular scheme
Regular_scheme
American WWII-era fighter aircraft
and IVAs in 1945. Postwar, a total of 150 Mustang P-51Ds were purchased and served in two regular (416 "Lynx" and 417 "City of Windsor") and six auxiliary
North_American_P-51_Mustang
Set with associative invertible operation
as the vertices on a regular n {\displaystyle n} -gon, as shown in blue in the image for n = 6 {\displaystyle n=6} . The group operation is multiplication
Group_(mathematics)
English mathematician (1904–1982)
MR 0986732 Abstract clone Commutator collecting process Isoclinism of groups Regular p-group Three subgroups lemma Hall algebra, and Hall polynomials Hall subgroup
Philip_Hall
Subdivision of the plane into polygons that are all regular
their wallpaper group symmetry. 1-uniform tilings include 3 regular tilings, and 8 semiregular ones, with 2 or more types of regular polygon faces. There
Euclidean tilings by convex regular polygons
Euclidean_tilings_by_convex_regular_polygons
Type of mathematical group
action on the hyperbolic plane, often exhibit particularly regular behaviour among Fuchsian groups and hyperbolic surfaces. A quaternion algebra over a field
Arithmetic_Fuchsian_group
{\displaystyle p^{6}} . For primes p > 3 {\displaystyle p>3} , the stem of Φ 6 {\displaystyle \Phi _{6}} consists of p + 7 {\displaystyle p+7} regular p-groups and
Artin_transfer_(group_theory)
composition X ↪ i P → p Y {\displaystyle X{\overset {i}{\hookrightarrow }}P{\overset {p}{\to }}Y} where i {\displaystyle i} is a regular embedding and p {\displaystyle
Regular_embedding
Linear representation in mathematics
field of characteristic p, the Steinberg representation has degree equal to the largest power of p dividing the order of the group. The Steinberg representation
Steinberg_representation
classified the regular homotopy classes of a k-sphere immersed in R n {\displaystyle \mathbb {R} ^{n}} – they are classified by homotopy groups of Stiefel
Regular_homotopy
Symmetric tessellation of a closed surface
underlying graph, or the automorphism group. Regular maps are typically defined and studied in three ways: topologically, group-theoretically, and graph-theoretically
Regular_map_(graph_theory)
Type of field extension
of algebra, a field extension L / k {\displaystyle L/k} is said to be regular if k is algebraically closed in L (i.e., k = k ^ {\displaystyle k={\hat
Regular_extension
Concept in differential equation mathematics
(Lazarus Fuchs 1866). When a is a regular singular point, which by definition means that p n − i ( z ) {\displaystyle p_{n-i}(z)} has a pole of order at
Regular_singular_point
Type of continuous map in topology
G=\operatorname {Aut} (p)} is considered as a discrete topological group. Every universal cover p : D → X {\displaystyle p:D\to X} is regular, with deck transformation
Covering_space
Group that admits a formal description in terms of reflections
Coxeter groups are precisely the finite Euclidean reflection groups; for example, the symmetry group of each regular polyhedron is a finite Coxeter group. However
Coxeter_group
Type of semigroup
quasi-periodic semigroup, group-bound semigroup, completely π-regular semigroup, strongly π-regular semigroup (sπr), or just π-regular semigroup (although the
Epigroup
In geometry, a convex polyhedron whose faces are regular polygons is known as a Johnson solid, or sometimes as a Johnson–Zalgaller solid. Some authors
List_of_Johnson_solids
Standings and Results for Group F of the Regular Season phase of the 2013–14 Eurocup basketball tournament. Source: Euroleague Basketball "Standings |
Eurocup 2013–14 Regular Season Group F
Eurocup_2013–14_Regular_Season_Group_F
Four-dimensional analogue of the cube
sequence of regular 4-polytopes and honeycombs, {p,3,3} with tetrahedral vertex figures, {3,3}. The tesseract is also in a sequence of regular 4-polytope
Tesseract
Symmetric subdivision in hyperbolic geometry
given below. There are infinitely many (p q 2) triangle group families. This article shows the regular tiling up to p, q = 8, and uniform tilings in 12 families:
Uniform tilings in hyperbolic plane
Uniform_tilings_in_hyperbolic_plane
Natural number
the first regular polygon that does not tile the plane with copies of itself. The pentagon solid has the largest face of any of the five regular three-dimensional
5
2023 Russian factional conflict
them as heroes. Putin also stated that members of the group who do not wish to become regular contractors were allowed to transfer to Belarus. On 3 July
Wagner_Group_rebellion
are called polygons. Regular polygons are equilateral and cyclic. A p-gonal regular polygon is represented by Schläfli symbol {p}. Many sources only consider
List_of_regular_polytopes
Group of symmetries of a regular polygon
mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest
Dihedral_group
In mathematics, a regular semigroup is a semigroup S in which every element is regular, i.e., for each element a in S there exists an element x in S such
Regular_semigroup
Infinite regular skew polyhedron
these regular skew apeirohedra {2q,2r|p} with extended chiral symmetry [[(p,q,p,r)]+] which he says is isomorphic to his abstract group (2q,2r|2,p). The
Regular_skew_apeirohedron
Tessellation of Euclidean space
A regular grid is a tessellation of n-dimensional Euclidean space by congruent parallelotopes (e.g. bricks). Its opposite is irregular grid. Grids of
Regular_grid
History of a branch of mathematics
finite soluble groups, and on the power-commutator structure of p-groups, including the ideas of regular p-groups and isoclinism of groups, which revolutionized
History_of_group_theory
Higman–Sims group, a subgroup of index two in the group of automorphisms of the Hoffman–Singleton graph. Take the M22 graph, a strongly regular graph srg(77
Higman–Sims_graph
Command-line utility for text search
searching text for lines that match a regular expression. Its name comes from the ed command g/re/p (global, regular expression, print), which has the same
Grep
Software library for interpreting regular expressions
Perl Compatible Regular Expressions (PCRE) is a library written in C, which implements a regular expression engine, inspired by the capabilities of the
Perl Compatible Regular Expressions
Perl_Compatible_Regular_Expressions
American investment management company
The Vanguard Group, Inc. is an American registered investment adviser founded on May 1, 1975, and based in Malvern, Pennsylvania, with approximately $12 trillion
The_Vanguard_Group
American writer (1890–1937)
Schultz, David E. (2001). An H.P. Lovecraft Encyclopedia (First ed.). Westport, Connecticut: Greenwood Publishing Group. ISBN 0-313-01682-8. OCLC 608158798
H._P._Lovecraft
Concept in mathematics
groups (the Coxeter groups or Weyl groups, including the symmetry groups of regular polyhedra). A (complex) reflection r (sometimes also called pseudo
Complex_reflection_group
Transformations induced by a mathematical group
topological groups on topological spaces, one also often considers smooth actions of Lie groups on smooth manifolds, regular actions of algebraic groups on algebraic
Group_action
Generalization of a polytope in real space
reflection groups, p. 431. Coxeter (1991), p. 131. Coxeter (1991), p. 126. Coxeter (1991), p. 125. Coxeter (1991), p. 180, Table VI. The regular honeycombs
Complex_polytope
Shape with nine sides
trisector. The regular enneagon has Dih9 symmetry, order 18. There are 2 subgroup dihedral symmetries: Dih3 and Dih1, and 3 cyclic group symmetries: Z9
Nonagon
Shape with five sides
regular convex polygon, the regular convex pentagon has a circumscribed circle. For a regular pentagon with successive vertices A, B, C, D, E, if P is
Pentagon
5-dimensional geometric object
by a space group and whose facets are uniform 4-polytopes. Regular 5-polytopes can be represented by the Schläfli symbol {p,q,r,s}, with s {p,q,r} polychoral
5-polytope
Shape with three equal sides
sides of equal length and three equal angles. It is a regular polygon, occasionally known as the regular triangle. It is a special case of an isosceles triangle
Equilateral_triangle
Polyhedron resulting from the snub operation
with the chiral octahedral group of symmetries is the snub cube. Only the icosahedron and the great icosahedron are also regular polyhedra. They are also
Snub_polyhedron
Shape with ten sides
The total sum of the interior angles of a simple decagon is 1440°. A regular decagon has all sides of equal length and each internal angle will always
Decagon
truncating the regular solids. The hemipolyhedra all have faces which pass through the origin. Their Wythoff symbols are of the form p p/m|q or p/m p/n|q. With
List of uniform polyhedra by Wythoff symbol
List_of_uniform_polyhedra_by_Wythoff_symbol
In number theory, measure of non-unique factorization
ideal class group (or class group) of an algebraic number field K {\displaystyle K} is the quotient group J K / P K {\displaystyle J_{K}/P_{K}} where J
Ideal_class_group
Group that is also a differentiable manifold with group operations that are smooth
groups of compact manifolds of larger dimension are regular Fréchet Lie groups; very little about their structure is known. The diffeomorphism group of
Lie_group
Polygons which have an accompanying imaginary dimension for each real dimension
In geometry, a regular complex polygon is a generalization of a regular polygon in real space to an analogous structure in a complex Hilbert space, where
Regular_complex_polygon
Notation for polytopes and tessellations
In geometry, the Schläfli symbol is a notation of the form {p,q,r, ...} that defines regular polytopes and tessellations. The Schläfli symbol is named after
Schläfli_symbol
Regular non-convex polygon
vertices, divided by 360°. The symmetry group of {p/q} is the dihedral group Dp, of order 2p, independent of q. Regular star polygons were first studied systematically
Star_polygon
American lawyer (1876–1943)
1–2 – via Newspapers.com. "Regular Democratic Ticket". El Paso Morning Times. Vol. 38, no. 317. El Paso, Texas. July 5, 1918. p. 10 – via Newspapers.com
Will_P._Brady
Variously-defined concept in geometry
In its original definition, it is a polyhedron with regular polygonal faces, and a symmetry group which is transitive on its vertices; today, this is
Semiregular_polyhedron
Concept in geometry
M., Regular Polytopes, §12.6 The number of reflections, equation 12.61 Regular polytopes, p. 233 George Lusztig, Introduction to Quantum Groups, Birkhauser
Coxeter_element
Poset representing certain properties of a polytope
the geometric figure will be a regular polytope. The group G of symmetries of a realization V of an abstract polytope P is generated by two reflections
Abstract_polytope
Group of geometric symmetries with at least one fixed point
Coxeter group, and like the polyhedral groups of 3D, it can be named by its related convex regular 4-polytope. Related pure rotational groups exist for
Point_group
Category whose objects are groups and whose morphisms are group homomorphisms
category G r p {\displaystyle \mathbf {Grp} } (or G p {\displaystyle \mathbf {Gp} } ) has the class of all groups for objects and group homomorphisms
Category_of_groups
Polyhedron with two kinds of faces
both the regular {p,q} and the dual regular {q,p}. A quasiregular polyhedron with this symbol will have a vertex configuration p.q.p.q (or (p.q)2). More
Quasiregular_polyhedron
Identity in group theory
that p-groups of small class are regular. The Hall–Petresco identity states that if x and y are elements of a group G and m is a positive integer then
Hall–Petresco_identity
4-regular undirected graph in mathematics
graph; its full automorphism group is isomorphic to the dihedral group of order 24, the group of symmetries of a regular dodecagon, including both rotations
Robertson_graph
Mathematical finite graph-associated function
1960s in the context of discrete subgroups of the two-by-two p-adic special linear group. Jean-Pierre Serre suggested in his book Trees that Ihara's original
Ihara_zeta_function
Polygonal chain whose vertices are not all coplanar
dimensions a regular skew polygon has vertices alternating between two parallel planes. A regular skew n-gon can be given a Schläfli symbol {p}#{} as a blend
Skew_polygon
Natural number
Regular Polytopes (3rd ed.). New York: Dover. pp. 18–19. Lounesto, Pertti (3 May 2001). Clifford Algebras and Spinors. Cambridge University Press. p. 216
8
American naval aviator (1915–1944)
been found. The 20th Fighter Group out of RAF Kings Cliffe, Northamptonshire had provided an escort of four North American P-51 Mustang fighters (two each
Joseph_P._Kennedy_Jr.
United States Navy component of JSOC
The Naval Special Warfare Development Group (NSWDG), abbreviated as DEVGRU ("Development Group") and unofficially known as SEAL Team Six, is the United
SEAL_Team_Six
Injective polynomial functions are bijective
C n {\displaystyle \mathbb {C} ^{n}} . The full theorem generalizes to regular maps on any algebraic variety over an algebraically closed field. Grothendieck's
Ax–Grothendieck_theorem
Shape with eleven sides
The regular hendecagon has Dih11 symmetry, order 22. Since 11 is a prime number there is one subgroup with dihedral symmetry: Dih1, and 2 cyclic group symmetries:
Hendecagon
Theorem in algebraic geometry
characteristic p > 0 for groups whose order is coprime to p, but can fail over fields of positive characteristic p > 0 when p divides the group order. For
Hurwitz's automorphisms theorem
Hurwitz's_automorphisms_theorem
One of two different regular graphs with 16 vertices
its spectrum. The 5-regular Clebsch graph is a Cayley graph with an automorphism group of order 1920, isomorphic to the Coxeter group D 5 {\displaystyle
Clebsch_graph
3D shape made of polyhedra sharing a common center
symmetry group acting transitively on its flags; the compound of two tetrahedra is the only regular compound with that property. There are five regular compounds
Polytope_compound
Type of topological group in mathematics
p {\displaystyle L^{p}} spaces can be generalized. Many of the results of finite group representation theory are proved by averaging over the group.
Locally_compact_group
Language family
Proto-Celtic language. The term "Celtic" was first used to describe this language group by Edward Lhuyd in 1707, following Paul-Yves Pezron, who made the explicit
Celtic_languages
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