Author:
García-Lucas Diego,del Río Ángel,Stanojkovski Mima
Abstract
AbstractLet p be a an odd prime and let G be a finite p-group with cyclic commutator subgroup $G^{\prime }$
G
′
. We prove that the exponent and the abelianization of the centralizer of $G^{\prime }$
G
′
in G are determined by the group algebra of G over any field of characteristic p. If, additionally, G is 2-generated then almost all the numerical invariants determining G up to isomorphism are determined by the same group algebras; as a consequence the isomorphism type of the centralizer of $G^{\prime }$
G
′
is determined. These claims are known to be false for p = 2.
Publisher
Springer Science and Business Media LLC
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