A generalization of the Arad–Ward theorem on Hall subgroups Full article
| Journal |
Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X |
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| Output data | Year: 2025, Volume: 679, Pages: 28-36 Pages count : 9 DOI: 10.1016/j.jalgebra.2025.05.001 | ||||
| Tags | Hall subgroup, Solvable group, Finite simple groups | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
Abstract:
For a set of primes π, denote by Eπ the class of finite groups containing a Hall π-subgroup. We establish that Eπ1 ∩Eπ2 is contained in Eπ1∩π2 . As a corollary, we prove that if π is a set of primes, l is an integer such that 2⩽l<|π|and Gis a finite group that contains a Hall ρ-subgroup for every subset ρof πof size l, then Gcontains a solvable Hall π-subgroup.
Cite:
Yang N.
, Buturlakin A.A.
A generalization of the Arad–Ward theorem on Hall subgroups
Journal of Algebra. 2025. V.679. P.28-36. DOI: 10.1016/j.jalgebra.2025.05.001 Scopus OpenAlex
A generalization of the Arad–Ward theorem on Hall subgroups
Journal of Algebra. 2025. V.679. P.28-36. DOI: 10.1016/j.jalgebra.2025.05.001 Scopus OpenAlex
Dates:
| Submitted: | Dec 28, 2024 |
| Published online: | May 19, 2025 |
| Published print: | Oct 1, 2025 |
Identifiers:
| Scopus: | 2-s2.0-105005110486 |
| OpenAlex: | W4410301415 |
Citing:
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