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Group algebras with unit group of class $p$

Zs. Balogh·A. Bovdi
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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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Zs. Balogh, A. Bovdi. 2005-07-18. Group algebras with unit group of class $p$. https://arxiv.org/abs/math/0507357

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