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locally finite group

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  • Locally finite group — In mathematics, in the field of group theory, a locally finite group is a type of group that can be studied in ways analogous to a finite group. Sylow subgroups, Carter subgroups, and abelian subgroups of locally finite groups have been… …   Wikipedia

  • Locally finite — The term locally finite has a number of different meanings in mathematics:*Locally finite collection of sets in a topological space *Locally finite group *Locally finite measure *Locally finite poset …   Wikipedia

  • Locally compact group — In mathematics, a locally compact group is a topological group G which is locally compact as a topological space. Locally compact groups are important because they have a natural measure called the Haar measure. This allows one to define… …   Wikipedia

  • Residually finite group — In the mathematical field of group theory, a group G is residually finite or finitely approximable if for every nontrivial element g in G there is a homomorphism h from G to a finite group, such that :h(g) eq 1.,There are a number of equivalent… …   Wikipedia

  • Group isomorphism — In abstract algebra, a group isomorphism is a function between two groups that sets up a one to one correspondence between the elements of the groups in a way that respects the given group operations. If there exists an isomorphism between two… …   Wikipedia

  • Group (mathematics) — This article covers basic notions. For advanced topics, see Group theory. The possible manipulations of this Rubik s Cube form a group. In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines …   Wikipedia

  • Group representation — In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group… …   Wikipedia

  • Group action — This article is about the mathematical concept. For the sociology term, see group action (sociology). Given an equilateral triangle, the counterclockwise rotation by 120° around the center of the triangle acts on the set of vertices of the… …   Wikipedia

  • Locally compact space — In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space.Formal definitionLet X be a topological space. The… …   Wikipedia

  • Group algebra — This page discusses topological algebras associated to topological groups; for the purely algebraic case of discrete groups see group ring. In mathematics, the group algebra is any of various constructions to assign to a locally compact group an… …   Wikipedia

  • Hall's universal group — In algebra, Hall s universal group isa countable locally finite group, say U , which is uniquely characterized by the following properties.* Every finite group G admits a monomorphism to U .* All such monomorphisms are conjugate by inner… …   Wikipedia

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