On Group Invariants Determined by Modular Group Algebras: Even Versus Odd Characteristic

Abstract Let p be a an odd prime and let G finite -group with cyclic commutator subgroup $G^{\prime }$ G ′ . We prove that the exponent abelianization of centralizer in are determined by group algebra over any field characteristic If, additionally, is 2-generated then almost all numerical invariants determining up to isomorphism same algebras; as consequence type determined. These claims known false for = 2.