Subgroup isomorphism problem for units of integral group rings

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5 Citations (Scopus)

Abstract

The Subgroup Isomorphism Problem for Integral Group Rings asks for which finite groups U it is true that if U is isomorphic to a subgroup of V(ZG), the group of normalized units of the integral group ring of the finite group G, it must be isomorphic to a subgroup of G. The smallest groups known not to satisfy this property are the counterexamples to the Isomorphism Problem constructed by M. Hertweck. However, the only groups known to satisfy it are cyclic groups of prime power order and elementary-abelian p-groups of rank 2. We give a positive solution to the Subgroup Isomorphism Problem for C4×C2. Moreover, we prove that if the Sylow 2-subgroup of G is a dihedral group, any 2-subgroup of V(ZG) is isomorphic to a subgroup of G.
Original languageEnglish
Pages (from-to)289-307
Number of pages19
JournalJ. Group Theory
Volume20
Issue number2
DOIs
Publication statusPublished - 2016

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