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Commutator subgroup — In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.[1][2] The commutator subgroup is important because it is the smallest… … Wikipedia
Class formation — In mathematics, a class formation is a structure used to organize the various Galois groups and modules that appear in class field theory. They were invented by Emil Artin and John Tate. Contents 1 Definitions 2 Examples of class formations 3 The … Wikipedia
Symmetric group — Not to be confused with Symmetry group. A Cayley graph of the symmetric group S4 … Wikipedia
Transfer (group theory) — In mathematics, the transfer in group theory is a group homomorphism defined given a finite group G and a subgroup H , which goes from the abelianization of G to that of H .FormulationTo define the transfer, take coset representatives for the… … Wikipedia
Alternating group — In mathematics, an alternating group is the group of even permutations of a finite set. The alternating group on the set {1,..., n } is called the alternating group of degree n , or the alternating group on n letters and denoted by A n or Alt( n… … Wikipedia
Adjoint functors — Adjunction redirects here. For the construction in field theory, see Adjunction (field theory). For the construction in topology, see Adjunction space. In mathematics, adjoint functors are pairs of functors which stand in a particular… … Wikipedia
Hurewicz theorem — In mathematics, the Hurewicz theorem is a basic result of algebraic topology, connecting homotopy theory with homology theory via a map known as the Hurewicz homomorphism. The theorem is named after Witold Hurewicz, and generalizes earlier… … Wikipedia
Hawaiian earring — In mathematics, the Hawaiian earring H is the topological space defined by the union of circles in the Euclidean plane R^2 with center (1/n,0) and radius 1/n for n=1,2,3,.... H is homeomorphic to the one point compactification of a countably… … Wikipedia
IA automorphism — In mathematics, in the realm of group theory, an IA automorphism of a group is an automorphism that acts as identity on the abelianization. The abelianization of a group is its quotient by its commutator subgroup. An IA automorphism is thus an… … Wikipedia
Superperfect group — In mathematics, in the realm of group theory, a group is said to be superperfect when its first two homology groups are trivial.The first homology group of a group is the abelianization of the group itself, since the homology of a group G is the… … Wikipedia
