Invariance of the Schur multiplier, the Bogomolov multiplier and the minimal number of generators under a variant of isoclinism

Ammu E. Antony, Sathasivam Kalithasan, Viji Z. Thomas

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce the q-Bogomolov multiplier as a generalization of the Bogomolov multiplier, and we prove that it is invariant under q-isoclinism. We prove that the q-Schur multiplier is invariant under q-exterior isoclinism, and as an easy consequence, we prove that the Schur multiplier is invariant under exterior isoclinism. We also prove that if and are groups with G / Z (G) ≅ H / Z (H) G/Z(G) H/Z(H), then the cardinalities of the minimal number of generators of and are the same. Moreover, we prove some structural results about non-abelian q-tensor square of groups.

Original languageEnglish
JournalJournal of Group Theory
DOIs
StateAccepted/In press - 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2023 Walter de Gruyter GmbH, Berlin/Boston.

ASJC Scopus subject areas

  • Algebra and Number Theory

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