Group algebras with unit group of class p

2005/07/18 by Zs. Balogh, A. Bovdi
Mathematics · #math.RA #math.GR #msc:16A46 #msc:16A26 #msc:20C05 #msc:19A22

paper · pdf

published as Publ. Math. Debrecen 65 (2004), no. 3-4, 261-268

arxiv created 2005/07/18 · arxiv updated 2009/12/01

Abstract

Let V(F_pG) be the group of normalized units of the group algebra F_pG of a finite nonabelian p-group G over the field F_p of p elements. Our goal is to investigate the power structure of V(F_pG), 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(F_pG) is isomorphic to V(F_pH) if and only if G and H are isomorphic.

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