group isomorphism

См. также в других словарях:

• 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 isomorphism problem — In abstract algebra, the group isomorphism problem is the decision problem of determining whether two group presentations present isomorphic groups.The isomorphism problem was identified by Max Dehn in 1911 as one of three fundamental decision… …   Wikipedia

• Isomorphism (disambiguation) — Isomorphism may refer to:* Isomorphism, in mathematics, a mapping that preserves the structure * Group isomorphism, in mathematics, a mapping that preserves the group structure * Ring isomorphism, in mathematics, a mapping that preserves both the …   Wikipedia

• Group — can refer to: Sociology * Group action (sociology) * Group behaviour * Groups of people, a description of various different human groups ** Peer group ** Workgroup * Group dynamics * Group (sociology), a sub set of a culture or of a society *… …   Wikipedia

• Isomorphism — In abstract algebra, an isomorphism (Greek: ἴσος isos equal , and μορφή morphe shape ) is a bijective map f such that both f and its inverse f −1 are homomorphisms, i.e., structure preserving mappings.In the more general setting of category… …   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

• Isomorphism problem — The isomorphism problem in mathematics may refer to* The graph isomorphism problem * The group isomorphism problem …   Wikipedia

• Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… …   Wikipedia

• Isomorphism theorem — In mathematics, specifically abstract algebra, the isomorphism theorems are three theorems that describe the relationship between quotients, homomorphisms, and subobjects. Versions of the theorems exist for groups, rings, vector spaces, modules,… …   Wikipedia

• Isomorphism of categories — In category theory, two categories C and D are isomorphic if there exist functors F : C rarr; D and G : D rarr; C which are mutually inverse to each other, i.e. FG = 1 D (the identity functor on D ) and GF = 1 C . This means that both the objects …   Wikipedia

• Group extension — In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence:1 ightarrow N… …   Wikipedia