Special Issue: International Conference on Group Theory "Combinatorial, Geometric and Dynamical Aspects of Infinite Groups"; Guest Editors: Laurent Bartholdi, Tullio Ceccherini-Silberstein, Tatiana Smirnova-Nagnibeda, Andrzej ŻukNo Access

MAXIMAL SUBGROUPS OF SOME NON LOCALLY FINITE p-GROUPS

E. L. PERVOVA

E. L. PERVOVA

Chelyabinsk State University, 129 ul. Br. Kashirinykh, 454021 Chelyabinsk, Russia

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https://doi.org/10.1142/S0218196705002803Cited by:11 (Source: Crossref)

Abstract

Kaplansky's conjecture claims that the Jacobson radical of a group algebra K[G], where K is a field of characteristic p > 0, coincides with its augmentation ideal if and only if G is a locally finite p-group. By a theorem of Passman, if G is finitely generated and then any maximal subgroup of G is normal of index p. In the present paper, we consider one infinite series of finitely generated infinite p-groups (hence not locally finite p-groups), so called GGS-groups. We prove that their maximal subgroups are nonetheless normal of index p. Thus these groups remain among potential counterexamples to Kaplansky's conjecture.

Keywords:

AMSC: 20F50, 20E28, 20E08

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