Group algebras with unit group of class $p$

Details Group algebras with unit group of class $p$ Group algebras with unit group of class $p$

2005-07-18

arxiv.org/abs/math/0507357v1

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

Mathematics

Rings and Algebras

Scientific paper

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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