Let p be a an odd prime and let G be a finite p-group with cyclic commutator subgroup G'. We prove that the exponent and the abelianization of the centralizer of 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' is determined. These claims are known to be false for p = 2.

On Group Invariants Determined by Modular Group Algebras: Even Versus Odd Characteristic / Garcia-Lucas, D; del Rio, A; Stanojkovski, M. - In: ALGEBRAS AND REPRESENTATION THEORY. - ISSN 1386-923X. - 2023, 26:(2023), pp. 2683-2707. [10.1007/s10468-022-10182-x]

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

Stanojkovski, M
2023-01-01

Abstract

Let p be a an odd prime and let G be a finite p-group with cyclic commutator subgroup G'. We prove that the exponent and the abelianization of the centralizer of 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' is determined. These claims are known to be false for p = 2.
2023
Garcia-Lucas, D; del Rio, A; Stanojkovski, M
On Group Invariants Determined by Modular Group Algebras: Even Versus Odd Characteristic / Garcia-Lucas, D; del Rio, A; Stanojkovski, M. - In: ALGEBRAS AND REPRESENTATION THEORY. - ISSN 1386-923X. - 2023, 26:(2023), pp. 2683-2707. [10.1007/s10468-022-10182-x]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/389349
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