Group algebras with unit group of class p
Abstract
Let V(FpG) be the group of normalized units of the group algebra FpG of a finite nonabelian p-group G over the field Fp of p elements. Our goal is to investigate the power structure of V(FpG), 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(FpG) is isomorphic to V(FpH) if and only if G and H are isomorphic.
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