On A-Groups with the Same Index Set as a Nilpotent Group Full article
| Journal |
Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X |
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| Output data | Year: 2026, Volume: 686, Pages: 836-844 Pages count : 9 DOI: 10.1016/j.jalgebra.2025.09.003 | ||||||
| Tags | Finite group, A-group, Conjugacy class | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования РФ | 075-15-2025-348 |
Abstract:
Let G be a finite group and N(G) be the set of conjugacy class sizes of G. For a prime p, let |G||p be the highest p-power dividing some element of N(G) and define |G|| = Πp∈π(G)|G||p. G is said to be an A-group if all its Sylow subgroups are abelian. We prove that if G is an A-group such that N(G) contains |G||p for every p ∈ π(G) as well as |G||, then G must be abelian. This result gives a positive answer to a question posed by Camina and Camina in 2006
Cite:
Zhou W.
, Gorshkov I.
On A-Groups with the Same Index Set as a Nilpotent Group
Journal of Algebra. 2026. V.686. P.836-844. DOI: 10.1016/j.jalgebra.2025.09.003 Scopus
On A-Groups with the Same Index Set as a Nilpotent Group
Journal of Algebra. 2026. V.686. P.836-844. DOI: 10.1016/j.jalgebra.2025.09.003 Scopus
Dates:
| Submitted: | Jun 20, 2025 |
| Published online: | Sep 17, 2025 |
| Published print: | Jan 15, 2026 |
Identifiers:
| Scopus: | 2-s2.0-105016144998 |
Citing:
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