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Gorenstein, D. (2012) Finite Groups. AMS Chelsea Publishing, American Mathematical Society, Providence.

has been cited by the following article:

  • TITLE: Artin Transfer Patterns on Descendant Trees of Finite p-Groups

    AUTHORS: Daniel C. Mayer

    KEYWORDS: Artin Transfer, Kernel Type, Target Type, Descendant Tree, Coclass Tree, Coclass Graph

    JOURNAL NAME: Advances in Pure Mathematics, Vol.6 No.2, January 29, 2016

    ABSTRACT: Based on a thorough theory of the Artin transfer homomorphism from a group G to the abelianization of a subgroup of finite index , and its connection with the permutation representation and the monomial representation of G, the Artin pattern , which consists of families , resp. , of transfer targets, resp. transfer kernels, is defined for the vertices of any descendant tree T of finite p-groups. It is endowed with partial order relations and , which are compatible with the parent-descendant relation of the edges of the tree T. The partial order enables termination criteria for the p-group generation algorithm which can be used for searching and identifying a finite p-group G, whose Artin pattern is known completely or at least partially, by constructing the descendant tree with the abelianization of G as its root. An appendix summarizes details concerning induced homomorphisms between quotient groups, which play a crucial role in establishing the natural partial order on Artin patterns and explaining the stabilization, resp. polarization, of their components in descendant trees T of finite p-groups.