Group algebras with unit group of class p

Zsolt Balogh, Adalbert Bovdi

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

Let V(script F signpG) be the group of normalized units of the group algebra script F signpG of a finite nonabelian p-group G over the field script F signp of p elements. Our goal is to investigate the power structure of V(script F signpG), when it has nilpotency class p. As a consequence, we have proved that if G and H are p-groups with cyclic Frattini subgroups and p > 2, then V(script F signpG) is isomorphic to V(script F signpH) if and only if G and H are isomorphic.

Original languageEnglish
Pages (from-to)261-268
Number of pages8
JournalPublicationes Mathematicae Debrecen
Volume65
Issue number3-4
Publication statusPublished - 2004
Externally publishedYes

Keywords

  • Group algebra
  • Group of units
  • Isomorphism problem

ASJC Scopus subject areas

  • General Mathematics

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