On the pronormality of subgroups of odd index in some direct products of finite groups
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
On the pronormality of subgroups of odd index in some direct products of finite groups
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| Автор |
Maslova, N. V.
Revin, D. O. |
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| Тематика |
DIRECT PRODUCT
FINITE GROUP ODD INDEX PRONORMAL SUBGROUP SIMPLE SYMPLECTIC GROUP WREATH PRODUCT |
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| Описание |
subgroup H of a group G is said to be pronormal in G if H and Hg are conjugate in (H,Hg) for each g ∈ G. Some problems in Finite Group Theory, Combinatorics and Permutation Group Theory were solved in terms of pronormality, therefore, the question of pronormality of a given subgroup in a given group is of interest. Subgroups of odd index in finite groups satisfy a native necessary condition of pronormality. In this paper, we continue investigations on pronormality of subgroups of odd index and consider the pronormality question for subgroups of odd index in some direct products of finite groups. In particular, in this paper, we prove that the subgroups of odd index are pronormal in the direct product G of finite simple symplectic groups over fields of odd characteristics if and only if the subgroups of odd index are pronormal in each direct factor of G. Moreover, deciding the pronormality of a given subgroup of odd index in the direct product of simple symplectic groups over fields of odd characteristics is reducible to deciding the pronormality of some subgroup H of odd index in a subgroup of Qt i=1 Z3 Symni , where each Symni acts naturally on {1, . . . ,ni}, such that H projects onto Qt i=1 Symni . Thus, in this paper, we obtain a criterion of pronormality of a subgroup H of odd index in a subgroup of Qt i=1 Zpi Symni , where each pi is a prime and each Symni acts naturally on {1, . . . , ni}, such that H projects onto Qt i=1 Symni . © 2023 World Scientific Publishing Company.
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| Дата |
2024-04-05T16:19:48Z
2024-04-05T16:19:48Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/submittedVersion |
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| Идентификатор |
Maslova, NV & Revin, DO 2023, 'On the pronormality of subgroups of odd index in some direct products of finite groups', Journal of Algebra and its Applications, Том. 22, № 04, 2350083. https://doi.org/10.1142/S0219498823500834
Maslova, N. V., & Revin, D. O. (2023). On the pronormality of subgroups of odd index in some direct products of finite groups. Journal of Algebra and its Applications, 22(04), [2350083]. https://doi.org/10.1142/S0219498823500834 0219-4988 Final All Open Access, Green https://www.scopus.com/inward/record.uri?eid=2-s2.0-85124829305&doi=10.1142%2fS0219498823500834&partnerID=40&md5=321a2aec3e6112bf489595494b8a14e6 https://arxiv.org/pdf/2003.09479 http://elar.urfu.ru/handle/10995/130403 10.1142/S0219498823500834 85124829305 000849400900001 |
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| Язык |
en
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| Права |
Open access (info:eu-repo/semantics/openAccess)
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| Формат |
application/pdf
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| Издатель |
World Scientific
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| Источник |
Journal of Algebra and Its Applications
Journal of Algebra and its Applications |
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