Symmetric subgroups in modular group algebras

zbMATH Open1115.16306arXiv0801.0809MaRDI QIDQ3441059

A. G. Tsapok, Olexandr Konovalov

Publication date: 29 May 2007

Abstract: Let V(KG) be a normalised unit group of the modular group algebra of a finite p-group G over the field K of p elements. We introduce a notion of symmetric subgroups in V(KG) as subgroups invariant under the action of the classical involution of the group algebra KG. We study properties of symmetric subgroups and construct a counterexample to the conjecture by V.Bovdi, which states that V(KG)=<G,S*>, where S* is a set of symmetric units of V(KG).

Full work available at URL: https://arxiv.org/abs/0801.0809

zbMATH Keywords

finite \(p\)-groupsmodular group algebrassymmetric unitsnormalised unit groupssubgroup invariants

Mathematics Subject Classification ID

Group rings (16S34) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Units, groups of units (associative rings and algebras) (16U60)

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