Group algebras with unit group of class $p$
Copyright policy )Group algebras with unit group of class $p$
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.
Frobenius induction, Burnside and representation rings, Units, groups of units (associative rings and algebras), Group rings, group algebras, isomorphism problem, 16A46, 16A26, 20C05, 19A22, Mathematics - Rings and Algebras, Group Theory (math.GR), Rings and Algebras (math.RA), Finite nilpotent groups, \(p\)-groups, FOS: Mathematics, groups of units, Mathematics - Group Theory, Group rings of finite groups and their modules (group-theoretic aspects)
Frobenius induction, Burnside and representation rings, Units, groups of units (associative rings and algebras), Group rings, group algebras, isomorphism problem, 16A46, 16A26, 20C05, 19A22, Mathematics - Rings and Algebras, Group Theory (math.GR), Rings and Algebras (math.RA), Finite nilpotent groups, \(p\)-groups, FOS: Mathematics, groups of units, Mathematics - Group Theory, Group rings of finite groups and their modules (group-theoretic aspects)
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