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Transformations induced by a mathematical group
In mathematics, an action of a group G {\displaystyle G} on a set S {\displaystyle S} is, loosely speaking, an operation that takes an element of G {\displaystyle
Group_action
Topics referred to by the same term
Look up Action or action in Wiktionary, the free dictionary. Action may refer to: Action (philosophy), something which is done by a person Action principles
Action
Topics referred to by the same term
Action Group may refer to: Action group (sociology), or task group, a group of people joined temporarily to accomplish some task or take part in some
Action_group
differential geometry, a Lie group action is a group action adapted to the smooth setting: G {\displaystyle G} is a Lie group, M {\displaystyle M} is a smooth
Lie_group_action
specifically geometric group theory, a geometric group action is a certain type of action of a discrete group on a metric space. In geometric group theory, a geometry
Geometric_group_action
geometry, an action of a group scheme is a generalization of a group action to a group scheme. Precisely, given a group S-scheme G, a left action of G on an
Group-scheme_action
Indian conglomerate
Action Group is an industrial conglomerate with expertise in manufacturing of the Action Shoes brand. Action Shoes is the most widely known business of
Action_Group_(conglomerate)
British direct action group
for, or displaying items in support of the group a criminal offence in the UK. The group uses direct action to disrupt the UK arms industry, which it accuses
Palestine_Action
Militant leftist group in France (1979–1987)
Germany is named Action Directe after the group. Lebanese Armed Revolutionary Factions Revolutionary Front for Proletarian Action (fr)Serge Cosseron
Action_Directe
In mathematics, an action of a group G on a topological space X is cocompact if the quotient space X/G is a compact space. If X is locally compact, then
Cocompact_group_action
American nonviolent organization against the war in Vietnam
A Quaker Action Group (AQAG) was founded in Philadelphia during the summer of 1966 to "apply nonviolent direct action as a witness against the war in Vietnam"
A_Quaker_Action_Group
an action group or task group is a group of people joined temporarily to accomplish some task or take part in some organized collective action. As the
Action_group_(sociology)
Topics referred to by the same term
Group action may refer to: Group action (mathematics) Group action (sociology) Action group (disambiguation) Class action, a type of lawsuit Collective
Group_action_(disambiguation)
Political party in Nigeria
The Action Group (AG) was a Nigerian nationalist political party established in Ibadan on 21 March 1951, by Chief Obafemi Awolowo. The party was founded
Action_Group_(Nigeria)
Coordinated social action by a group of people
sociology, a group action is a situation in which a number of agents take action simultaneously in order to achieve a common goal; their actions are usually
Group_action_(sociology)
Concept in group theory
group action is sharply 2-transitive if such g ∈ G {\displaystyle g\in G} is unique. A 2-transitive group is a group such that there exists a group action
Multiply transitive group action
Multiply_transitive_group_action
Group whose operation is composition of permutations
permutation group permute the elements of the set is called its group action. Group actions have applications in the study of symmetries, combinatorics and
Permutation_group
Irish advocacy group
Divorce Action Group (Irish: Grúpa Gníomhaíochta Colscartha) was an Irish organisation campaigning for the legalisation of divorce in Ireland. The group was
Divorce_Action_Group
In topology, a continuous group action on a topological space X is a group action of a topological group G that is continuous: i.e., G × X → X , ( g ,
Continuous_group_action
Student organization campaigning for civil rights
The Nonviolent Action Group (NAG) was a student-run campus organization at Howard University that campaigned against racial segregation and other civil
Nonviolent_Action_Group
Tool in symplectic geometry
associated with a Hamiltonian action of a Lie group on a symplectic manifold, used to construct conserved quantities for the action. The momentum map generalizes
Momentum_map
Book by Mancur Olson
The Logic of Collective Action: Public Goods and the Theory of Groups is a book by Mancur Olson Jr. published in 1965. It develops a theory of political
The Logic of Collective Action
The_Logic_of_Collective_Action
Concept in theoretical physics
this group property: as the scale μ varies, the theory presents self-similarly, and any scale can be accessed from any other scale by this group action. More
Renormalization_group
Branch of mathematics that studies the properties of groups
group acts on the n-dimensional vector space Kn by linear transformations. This action makes matrix groups conceptually similar to permutation groups
Group_theory
In group theory, equivalence class under the relation of conjugation
automorphism. Another way to illustrate the conjugacy action is by considering the general linear group GL ( n ) {\displaystyle \operatorname {GL} (n)}
Conjugacy_class
Organization
The Positive Action Group (PAG) (Manx: Possan Jantys Jarrooagh) is a political pressure group formed on the Isle of Man in November 2006. They see that
Positive_Action_Group
Physical theory with fields invariant under the action of local "gauge" Lie groups
the action of the (non-abelian) SU(2) symmetry group on the isospin doublet of protons and neutrons. This is similar to the action of the U(1) group on
Gauge_theory
Group actions are central to Riemannian geometry and defining orbits (control theory). The orbits of computational anatomy consist of anatomical shapes
Group actions in computational anatomy
Group_actions_in_computational_anatomy
Not-for profit association
The Automotive Industry Action Group (AIAG) is a not-for-profit association founded in 1982 and based in Southfield, Michigan. It was originally created
Automotive Industry Action Group
Automotive_Industry_Action_Group
U.S.-based non-profit organization
Treatment Action Group (TAG) is a U.S.-based organization that has been prominent within the movement of HIV/AIDS activism. Being formed in 1991, it has
Treatment_Action_Group
American line of action figures and media franchise
forces with the Action Soldier (U.S. Army), Action Sailor (U.S. Navy), Action Pilot (U.S. Air Force), Action Marine (U.S. Marine Corps), Action lifeline (U
G.I._Joe
Dedicated group of US policy-makers
The Iran Action Group was formed on Thursday, 16 August 2018 by United States Secretary of State Mike Pompeo as a dedicated group to coordinate and run
Iran_Action_Group
UK charity that works to alleviate poverty and social exclusion
Child Poverty Action Group (CPAG) is a UK charity that works to alleviate poverty and social exclusion. The Group first met on 5 March 1965, at a meeting
Child_Poverty_Action_Group
Indian counter-terrorism unit
The 51 Special Action Group is a special response unit of the National Security Guard (NSG) of India. It was raised by the Cabinet Secretariat under the
51_Special_Action_Group
Set with associative invertible operation
for a deeper understanding of groups. It studies the group by its group actions on other spaces. A broad class of group representations are linear representations
Group_(mathematics)
Group whose operation is a composition of braids
Cartesian product of X {\displaystyle X} ) by the permutation action of the symmetric group on n {\displaystyle n} strands operating on the indices of coordinates
Braid_group
The Towpath Action Group (TAG) is a waterway society in the United Kingdom, campaigning for better access to towpaths. The group started in Manchester
Towpath_Action_Group
American rock bank (2004–2010)
Action Action was an American indie rock band, formerly signed to Victory Records. Action Action was formed in 2004 by members of The Reunion Show, Count
Action_Action
Type of naval fleet with an aircraft carrier
referred to as a battleship battle group. It was alternately referred to as a surface action group. The battleship battle group typically consisted of one modernized
Carrier_battle_group
Polynomial in combinatorial mathematics
cycle index polynomial of a permutation group, one can enumerate equivalence classes due to the group's action. This is the main ingredient in the Pólya
Cycle_index
Neighbourhood Action Group, or NAG, is a UK initiative, set up to deal with key issues identified by a community's first public consultation. The group is coordinated
Neighbourhood_action_group
Subgroup of the group of invertible n×n matrices
satisfies the axioms of a group action. As in other types of group theory, it is important to study group actions, since groups arise naturally as symmetries
Linear_algebraic_group
Type of social dilemma
Collective Action. Problems arise when too many group members choose to pursue individual profit and immediate satisfaction rather than behave in the group's best
Collective_action_problem
Action figure
Action Man is an action figure brand launched in the United Kingdom in 1966 by Palitoy as a licensed copy of Hasbro's American "movable fighting man"
Action_Man
Group that is a topological space with continuous group operations
defined on a very wide class of topological groups. Topological groups, along with continuous group actions, are used to study continuous symmetries, which
Topological_group
Type of lawsuit
A class action, also known as a class-action lawsuit, class suit, or representative action, is a type of lawsuit where a person or small group of people
Class_action
Sporadic simple group
Suzuki group. Elements of the monster are stored as words in the elements of H and an extra generator T. It is reasonably quick to calculate the action of
Monster_group
Mathematical behavior near singularities
\gamma } . This construction gives a well-defined left group action of the fundamental group π 1 ( X , x ) {\displaystyle \pi _{1}(X,x)} on the base
Monodromy
New Zealand white nationalist group
Action Zealandia is a white nationalist group in New Zealand that emerged following the Christchurch mosque shootings in 2019 as the successor to an earlier
Action_Zealandia
Electoral list
Carlo Calenda. During the 19th legislature, it named its parliamentary group Action – Italia Viva – Renew Europe in the Chamber and the Senate. Following
Action_–_Italia_Viva
2025 South Korean television series
합류 [Joo Yeon-woo, this time an action comedy... A series of ever-changing characters in the cast of Tving's 'Study Group'] (in Korean). SPOTV. Archived
Study_Group_(TV_series)
Act which takes other individuals into account
In sociology, social action, also known as Weberian social action, is an act which takes into account the actions and reactions of individuals (or 'agents')
Social_action
Mathematical group
is itself a symplectic manifold. A transformation under an action of the symplectic group is thus, in a sense, a linearised version of a symplectomorphism
Symplectic_group
The Consumer Action Group (CAG) is a UK forum which provides free help and support on all consumer issues. It is the U.K.'s National Consumer Service It
Consumer_Action_Group
Late 20th century campaign group in County Clare, Ireland
The Burren Action Group was a group of people from County Clare in Ireland who opposed plans during the 1990s by the Office of Public Works to develop
Burren_Action_Group
Film genre
The action film is a film genre that predominantly features chase sequences, fights, shootouts, explosions, and stunt work. The specifics of what constitutes
Action_film
Tools for studying groups based on techniques from algebraic topology
representations, group cohomology looks at the group actions of a group G in an associated G-module M to elucidate the properties of the group. By treating
Group_cohomology
Group that is also a differentiable manifold with group operations that are smooth
action provides a measure of rigidity and yields a rich algebraic structure. The presence of continuous symmetries expressed via a Lie group action on
Lie_group
Policies aiming to increase inclusion of people from marginalized groups
for certain groups Marketing/advertising to groups that the affirmative action is intended to increase Specific training or emulation actions for identified
Affirmative_action
Conjecture in topology
Restricting to groups G which are locally compact and have a continuous, faithful group action on M, the conjecture states that G must be a Lie group. Because
Hilbert–Smith_conjecture
Grupo Ação Lésbica Feminista (English: Feminist Lesbian Action Group, abbreviated as GALF) was one of the first organizations of the Homosexual Brazilian
Feminist_Lesbian_Action_Group
Group of flat spacetime symmetries
The Poincaré group, named after Henri Poincaré (1905), was first defined by Hermann Minkowski (1908) as the isometry group of Minkowski spacetime. It
Poincaré_group
In group theory, a branch of mathematics, an opposite group is a way to construct a group from another group that allows one to define right action as
Opposite_group
Coalition of aviation industry experts focusing on sustainable development issues
The Air Transport Action Group (ATAG) is a coalition of aviation industry experts focusing on sustainable development issues. Its board of directors is
Air_Transport_Action_Group
Action of a semigroup on a set
semigroup action is a generalization of the notion of a group action in group theory. From the computer science point of view, semigroup actions are closely
Semigroup_action
Environmental justice organization
The Action Group on Erosion, Technology, and Concentration (ETC), pronounced "et cetera," is an advocacy organization based around "the conservation and
ETC_Group_(eco-justice)
Group with subnormal series where all factors are abelian
specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently
Solvable_group
mathematics, an action groupoid or a transformation groupoid is a groupoid that expresses a group action. Namely, given a (right) group action X × G → X ,
Action_groupoid
Type of group in abstract algebra
Subgroups of symmetric groups are called permutation groups and are widely studied because of their importance in understanding group actions, homogeneous spaces
Symmetric_group
Mechanism that activates a gun
the trigger group), colloquially it is usually used to refer specifically to the trigger blade. Most firearm triggers are "single-action", meaning that
Trigger_(firearms)
Property that is not changed by mathematical transformations
unchanged, "invariant" under the group action, or under an element g of the group. Frequently, one will have a group acting on a set X, which leaves one
Invariant_(mathematics)
acting groups are measurable groups themselves. If S = G {\displaystyle S=G} , and the group action is the group law, then a measurable group is a group G
Measurable_acting_group
Event done by an agent for a purpose
In philosophy, an action is something an agent does. Actions contrast with events that merely happen to someone and are typically performed for a purpose
Action_(philosophy)
American hip-hop group
C.I.A., a name short for Cru’In Action!, replacing the earlier name Stereo Crew, was an American hip-hop trio, K-Dee, Sir Jinx, and Ice Cube, on the Los
C.I.A._(band)
Non-profit organization in Michigan, United States
The Education Action Group Foundation (EAG) is a nonprofit organization located in Michigan with a mission focused on increasing educational choice and
Education Action Group Foundation
Education_Action_Group_Foundation
The Baltic Sea Action Group (BSAG) is an independent non-profit foundation based in Finland. Formed in 2008, it seeks to restore the Baltic Sea, one of
Baltic_Sea_Action_Group
Mathematical group that can be generated as the set of powers of a single element
In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently Z {\displaystyle \mathbb {Z} } n or Zn, not to be confused
Cyclic_group
Commutative group (mathematics)
an abelian group,[note 1] also called a commutative group, is a group in which the result of applying the group operation to two group elements does
Abelian_group
The following is a partial list of direct action groups. Some groups known for their use of direct action include: ADAPT AIDS Coalition to Unleash Power
List_of_direct_action_groups
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
{\displaystyle M} in a way that generalizes the properties of the action of Kleinian group by Möbius transformations on the ideal boundary S 2 {\displaystyle
Convergence_group
Lie group of complex numbers of unit modulus; topologically a circle
mathematics, the circle group, denoted by T {\displaystyle \mathbb {T} } or S 1 {\displaystyle S^{1}} , is the multiplicative group of all complex numbers
Circle_group
Philippine military contingent sent in Vietnam War
The Philippine Civic Action Group – Vietnam (PHILCAG–V) was the Armed Forces of the Philippines contingent sent to the Republic of Vietnam or South Vietnam
Philippine_Civic_Action_Group
Written and visual fiction genre
and action games. It includes martial arts action, extreme sports action, car chases and vehicles, hand-to-hand combat, suspense action, and action comedy
Action_fiction
Loyalist group in County Cork (1920–1922)
The Loyalist Action Group was a secret loyalist group active in County Cork during the Irish War of Independence. It was made up of local Protestant unionists
Loyalist_Action_Group
Political party in Namibia
The Monitor Action Group is a political party in Namibia. The party came into existence as the transformation of the National Party of South West Africa
Monitor_Action_Group
Construction in group theory
the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action of the
Projective_linear_group
Spanish anarchist militant group (1973–1979)
The Internationalist Revolutionary Action Groups (French: Groupes d'action révolutionnaires internationalistes; Spanish: Grupos de Acción Revolucionaria
Internationalist Revolutionary Action Groups
Internationalist_Revolutionary_Action_Groups
Non-commutative group with 6 elements
order RGB. The symmetric group S3 is then the group of all possible rearrangements of these blocks. If we denote by a the action "swap the first two blocks"
Dihedral_group_of_order_6
Group homomorphism into the general linear group over a vector space
homomorphism from G to the symmetric group SX of X. For more information on this topic see the article on group action. Every group G can be viewed as a category
Group_representation
Type of group used in topology and geometric group theory
In mathematics, a CAT(0) group is a finitely generated group with a group action on a CAT(0) space that is geometrically proper, cocompact, and isometric
CAT(0)_group
Concept in mathematics
x+\mathbb {Z} ^{2}\mapsto Ax+\mathbb {Z} ^{2}} . The action of diffeomorphisms on the first homology group of T 2 {\displaystyle \mathbb {T} ^{2}} gives a
Mapping class group of a surface
Mapping_class_group_of_a_surface
Group of unitary complex matrices with determinant of 1
unitary group of degree n, denoted SU(n), is the Lie group of n × n unitary matrices with determinant 1. The matrices of the more general unitary group may
Special_unitary_group
Former American amusement park in New Jersey
Action Park was an amusement and water park located in Vernon Township, New Jersey, United States, on the grounds of the Vernon Valley/Great Gorge ski
Action_Park
Political party in Germany
Action Group of Independent Germans (German: Aktionsgemeinschaft Unabhängiger Deutscher, or AUD) was a nationalist-neutralist party in the West Germany
Action Group of Independent Germans
Action_Group_of_Independent_Germans
Concept in mathematics regarding sets operating on groups
an operator-subgroup relative to the operator set X, of the group in question. Group action Bourbaki 1974, p. 31. Bourbaki 1974, pp. 30–31. Mac Lane 1998
Group_with_operators
Education Action Groups were set up at most New Zealand university campuses during the 1990s as a vehicle for direct action against user pays reforms
Education_Action_Group
Category where every morphism is invertible; generalization of a group
comes with an equivalence relation, G-set: a set equipped with an action of a group G {\displaystyle G} . Groupoids are often used to reason about
Groupoid
Group within the Commonwealth of Nations
The Commonwealth Ministerial Action Group on the Harare Declaration, abbreviated to CMAG, is a group of representatives of members of the Commonwealth
Commonwealth Ministerial Action Group
Commonwealth_Ministerial_Action_Group
Concept in mathematics
field k as an algebraic group, which are actions of G on k-vector spaces. Also, one can study the complex representations of the group G(k) when k is a finite
Reductive_group
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