The size of a minimal generating set for primitive 3/2-transitive groups Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2022, Volume: 63, Number: 6, Pages: 1041-1048 Pages count : 8 DOI: 10.1134/S0037446622060039 | ||||||
| Tags | 2-homogeneous group; 2-transitive group; 3/2-transitive group; Frobenius complement; minimal generating set; primitive permutation group | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
Abstract:
We refer to d(G) as the minimal size of a generating set ofa finite group G, and say that G is d -generated if d(G)≤ d.A transitive permutation group G is called 3/2-transitive ifthe point stabilizer Gαis nontrivial and its orbits distinct from α are of the same size.We prove that d(G)≤ 4 for every primitive 3/2-transitive permutation group G and, moreover,G is 2-generated except for the rather particular solvable affine groupsthat we describe completely.In particular, all finite 2-transitive and 2-homogeneous groups are 2-generated.We also show that every finite group whose abelian subgroups are cyclic is 2-generated,and so is every Frobenius complement. © 2022, Pleiades Publishing, Ltd.
Cite:
Vasil'ev A.V.
, Zvezdina M.A.
, Churikov D.V.
The size of a minimal generating set for primitive 3/2-transitive groups
Siberian Mathematical Journal. 2022. V.63. N6. P.1041-1048. DOI: 10.1134/S0037446622060039 WOS Scopus РИНЦ OpenAlex
The size of a minimal generating set for primitive 3/2-transitive groups
Siberian Mathematical Journal. 2022. V.63. N6. P.1041-1048. DOI: 10.1134/S0037446622060039 WOS Scopus РИНЦ OpenAlex
Original:
Васильев А.В.
, Звездина М.А.
, Чуриков Д.В.
Размер минимального порождающего множества примитивной 3/2-транзитивной группы
Сибирский математический журнал. 2022. Т.63. №6. С.1213-1223. DOI: 10.33048/smzh.2022.63.603 РИНЦ
Размер минимального порождающего множества примитивной 3/2-транзитивной группы
Сибирский математический журнал. 2022. Т.63. №6. С.1213-1223. DOI: 10.33048/smzh.2022.63.603 РИНЦ
Dates:
| Submitted: | May 28, 2022 |
| Accepted: | Aug 15, 2022 |
Identifiers:
| Web of science: | WOS:000896024900003 |
| Scopus: | 2-s2.0-85143590953 |
| Elibrary: | 58890880 |
| OpenAlex: | W4311080303 |
Citing:
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