English

Group algebras with unit group of class $p$

Rings and Algebras 2007-05-23 v1 Group Theory

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.

Keywords

Cite

@article{arxiv.math/0507357,
  title  = {Group algebras with unit group of class $p$},
  author = {Zs. Balogh and A. Bovdi},
  journal= {arXiv preprint arXiv:math/0507357},
  year   = {2007}
}
R2 v1 2026-07-22T17:22:14.308Z