Symmetric subgroups in modular group algebras

Alexander Konovalov, A. G. Krivokhata

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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).
Original languageEnglish
Number of pages5
JournalNauk. Visn. Uzhgorod. Univ., Ser. Mat.,
Volume9
Publication statusPublished - 5 Jan 2008

Keywords

  • math.RA
  • math.GR
  • 16S34
  • 20C05
  • Rings and Algebras
  • Group Theory

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