endomorphism group

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• Endomorphism — In mathematics, an endomorphism is a morphism (or homomorphism) from a mathematical object to itself. For example, an endomorphism of a vector space V is a linear map ƒ: V → V and an endomorphism of a group G is a group homomorphism ƒ: G → G ,… …   Wikipedia

• Endomorphism ring — In abstract algebra, one associates to certain objects a ring, the object s endomorphism ring, which encodes several internal properties of the object. We will start with the example of abelian groups. Suppose A is an abelian group. As the name… …   Wikipedia

• Group homomorphism — In mathematics, given two groups ( G , *) and ( H , ·), a group homomorphism from ( G , *) to ( H , ·) is a function h : G → H such that for all u and v in G it holds that: h(u*v) = h(u) h(v) where the group operation on the left hand side of the …   Wikipedia

• Group ring — This page discusses the algebraic group ring of a discrete group; for the case of a topological group see group algebra, and for a general group see Group Hopf algebra. In algebra, a group ring is a free module and at the same time a ring,… …   Wikipedia

• Group with operators — In abstract algebra, a branch of pure mathematics, the algebraic structure group with operators or Ω group is a group with a set of group endomorphisms.Groups with operators were extensively studied by Emmy Noether and her school in the 1920s.… …   Wikipedia

• Group cohomology — This article is about homology and cohomology of a group. For homology or cohomology groups of a space or other object, see Homology (mathematics). In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well… …   Wikipedia

• Group code — In computer science, group codes are a type of code. Group codes consist of n linear block codes which are subgroups of G^n, where G is a finite Abelian group.A systematic group code C is a code over G^n of order left| G ight|^k defined by n k… …   Wikipedia

• Cyclic group — Group theory Group theory …   Wikipedia

• Frobenius endomorphism — In commutative algebra and field theory, which are branches of mathematics, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of rings with prime characteristic p , a class importantly including fields. The… …   Wikipedia

• Adjoint endomorphism — In mathematics, the adjoint endomorphism or adjoint action is an endomorphism of Lie algebras that plays a fundamental role in the development of the theory of Lie algebras and Lie groups.Given an element x of a Lie algebra mathfrak{g}, one… …   Wikipedia

• Retract (group theory) — In mathematics, in the field of group theory, a subgroup of a group is termed a retract if there is an endomorphism of the group that maps surjectively to the subgroup and is identity on the subgroup. In symbols, H is a retract of G if and only… …   Wikipedia