A criterion for nonsolvability of a finite group and recognition of direct squares of simple groups Full article
| Journal |
Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302 |
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| Output data | Year: 2022, Volume: 61, Number: 4, Pages: 288-300 Pages count : 13 DOI: 10.1007/s10469-023-09697-z | ||||||
| Tags | criterion of nonsolvability, simple exceptional group, element orders, recognition by spectrum, algebra, mathematical logic and foundations | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
Abstract:
The spectrum ω(G) of a finite group G is the set of orders of its elements. The following sufficient criterion of nonsolvability is proved: if, among the prime divisors of the order of a group G, there are four different primes such that ω(G) contains all their pairwise products but not a product of any three of these numbers, then G is nonsolvable. Using this result, we show that for q ⩾ 8 and q ≠ 32, the direct square Sz(q) × Sz(q) of the simple exceptional Suzuki group Sz(q) is uniquely characterized by its spectrum in the class of finite groups, while for Sz(32) × Sz(32), there are exactly four finite groups with the same spectrum.
Cite:
Wan Z.
, Vasil'ev A.V.
, Grechkoseeva M.A.
, Zhurtov A.K.
A criterion for nonsolvability of a finite group and recognition of direct squares of simple groups
Algebra and Logic. 2022. V.61. N4. P.288-300. DOI: 10.1007/s10469-023-09697-z WOS Scopus РИНЦ OpenAlex
A criterion for nonsolvability of a finite group and recognition of direct squares of simple groups
Algebra and Logic. 2022. V.61. N4. P.288-300. DOI: 10.1007/s10469-023-09697-z WOS Scopus РИНЦ OpenAlex
Original:
Ван Д.
, Васильев А.В.
, Гречкосеева М.А.
, Журтов А.Х.
Условие неразрешимости конечной группы и распознавание прямых квадратов простых групп
Алгебра и логика. 2022. Т.61. №4. С.424-442. DOI: 10.33048/alglog.2022.61.403 РИНЦ
Условие неразрешимости конечной группы и распознавание прямых квадратов простых групп
Алгебра и логика. 2022. Т.61. №4. С.424-442. DOI: 10.33048/alglog.2022.61.403 РИНЦ
Dates:
| Submitted: | Feb 1, 2022 |
| Published print: | Apr 5, 2023 |
| Published online: | Apr 5, 2023 |
Identifiers:
| Web of science: | WOS:000982080600002 |
| Scopus: | 2-s2.0-85151554203 |
| Elibrary: | 59282576 |
| OpenAlex: | W4362610464 |