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 𝐺 and 𝐻 are 𝑝-groups with
Funding source: Science and Engineering Research Board
Award Identifier / Grant number: MTR/2020/000483
Funding statement: Viji Z. Thomas acknowledges research support from SERB, DST, Government of India grant MTR/2020/000483. Sathasivam K. acknowledges the Ministry of Education, Government of India, for the doctoral fellowship under the Prime Minister’s Research Fellows (PMRF) scheme.
Acknowledgements
We thank the anonymous referees for their valuable comments which improved the exposition greatly.
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Communicated by: Bettina Eick
References
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Virtual planar braid groups and permutations
- Orders on free metabelian groups
- The Reidemeister spectrum of direct products of nilpotent groups
- Structure of the Macdonald groups in one parameter
- Finite groups with modular 𝜎-subnormal subgroups
- Invariance of the Schur multiplier, the Bogomolov multiplier and the minimal number of generators under a variant of isoclinism
- An exact sequence for the graded Picent
Artikel in diesem Heft
- Frontmatter
- Virtual planar braid groups and permutations
- Orders on free metabelian groups
- The Reidemeister spectrum of direct products of nilpotent groups
- Structure of the Macdonald groups in one parameter
- Finite groups with modular 𝜎-subnormal subgroups
- Invariance of the Schur multiplier, the Bogomolov multiplier and the minimal number of generators under a variant of isoclinism
- An exact sequence for the graded Picent