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
Reference49 articles.
1. Bagiński, C.: The isomorphism question for modular group algebras of metacyclic p-groups. Proc. Amer. Math. Soc. 104(1), 39–42 (1988)
2. Bagiński, C.: On the isomorphism problem for modular group algebras of elementary abelian-by-cyclic p-groups. Colloq. Math. 82(1), 125–136 (1999)
3. Bagiński, C., Caranti, A.: The modular group algebras of p-groups of maximal class. Canad. J. Math. 40(6), 1422–1435 (1988)
4. Broche, O., del Río, Á.: The Modular Isomorphism Problem for two generated groups of class two. Indian J. Pure Appl. Math. 52, 721–728 (2021)
5. Broche, O., García-Lucas, D., del Río, Á.: A classification of the finite two-generated cyclic-by-abelian groups of prime power order, arXiv:2106.06449
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献