On π-Solvable and Locally π-Solvable Groups with Factorization
We prove that, in a locally π-solvable group G = AB with locally normal subgroups A and B, there exist pairwise-permutable Sylow π′- and p-subgroups A π′, A p and B π′, B p , p ∈ π, of the subgroups A and B, respectively, such that A π′ B π′ is a Sylow π′-subgroup of the group G and, for an arbit...
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| Date: | 2001 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2001
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4304 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510436036706304 |
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| author | Putilov, S. V. Chernikov, N. S. Путилов, С. В. Черников, Н. С. Путилов, С. В. Черников, Н. С. |
| author_facet | Putilov, S. V. Chernikov, N. S. Путилов, С. В. Черников, Н. С. Путилов, С. В. Черников, Н. С. |
| author_sort | Putilov, S. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:25:59Z |
| description | We prove that, in a locally π-solvable group G = AB with locally normal subgroups A and B, there exist pairwise-permutable Sylow π′- and p-subgroups A π′, A p and B π′, B p , p ∈ π, of the subgroups A and B, respectively, such that A π′ B π′ is a Sylow π′-subgroup of the group G and, for an arbitrary nonempty set σ \( \subseteq \) π, $$\left( {\prod\nolimits_{p \in {\sigma }} {A_p } } \right)\left( {\prod\nolimits_{p \in {\sigma }} {B_p } } \right)\quad {and}\quad \left( {A_{{\pi }\prime } \prod\nolimits_{p \in {\sigma }} {A_p } } \right)\left( {B_{{\pi }\prime } \prod\nolimits_{p \in {\sigma }} {B_p } } \right)$$ are Sylow σ- and π′ ∪ σ-subgroups, respectively, of the group G. |
| first_indexed | 2026-03-24T02:56:58Z |
| format | Article |
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| id | umjimathkievua-article-4304 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:56:58Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b8/75c2899050c1f80986e99128462cd9b8.pdf |
| spelling | umjimathkievua-article-43042020-03-18T20:25:59Z On π-Solvable and Locally π-Solvable Groups with Factorization О π-разрешимых и локально π-разрешимых группах с факторизацией Putilov, S. V. Chernikov, N. S. Путилов, С. В. Черников, Н. С. Путилов, С. В. Черников, Н. С. We prove that, in a locally π-solvable group G = AB with locally normal subgroups A and B, there exist pairwise-permutable Sylow π′- and p-subgroups A π′, A p and B π′, B p , p ∈ π, of the subgroups A and B, respectively, such that A π′ B π′ is a Sylow π′-subgroup of the group G and, for an arbitrary nonempty set σ \( \subseteq \) π, $$\left( {\prod\nolimits_{p \in {\sigma }} {A_p } } \right)\left( {\prod\nolimits_{p \in {\sigma }} {B_p } } \right)\quad {and}\quad \left( {A_{{\pi }\prime } \prod\nolimits_{p \in {\sigma }} {A_p } } \right)\left( {B_{{\pi }\prime } \prod\nolimits_{p \in {\sigma }} {B_p } } \right)$$ are Sylow σ- and π′ ∪ σ-subgroups, respectively, of the group G. Доводиться, що в локально π-розв'язній групі $G = AB$ із локально нормальними підгрупами $A$ і $B$ і існують попарно переставні силовські π'- і $p$-підгрупи $A_{π'}$ і $А_р$, $B_{π'}$ і $B_р$, $р є π$, відповідно підгруп $A$ і $B$ такі, що є силовською π'-підгрупою групи $G$ та для довільної непорожньої множини $σ ⊆ π$ $$\left( {\prod\nolimits_{p \in {\sigma }} {A_p } } \right)\left( {\prod\nolimits_{p \in {\sigma }} {B_p } } \right)\quad {and}\quad \left( {A_{{\pi }\prime } \prod\nolimits_{p \in {\sigma }} {A_p } } \right)\left( {B_{{\pi }\prime } \prod\nolimits_{p \in {\sigma }} {B_p } } \right)$$ є силовськими відповідно $σ-$ і $π′ ∪ σ$ -підгрупами групи $G$. Institute of Mathematics, NAS of Ukraine 2001-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4304 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 6 (2001); 840-846 Український математичний журнал; Том 53 № 6 (2001); 840-846 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4304/5312 https://umj.imath.kiev.ua/index.php/umj/article/view/4304/5313 Copyright (c) 2001 Putilov S. V.; Chernikov N. S. |
| spellingShingle | Putilov, S. V. Chernikov, N. S. Путилов, С. В. Черников, Н. С. Путилов, С. В. Черников, Н. С. On π-Solvable and Locally π-Solvable Groups with Factorization |
| title | On π-Solvable and Locally π-Solvable Groups with Factorization |
| title_alt | О π-разрешимых и локально π-разрешимых группах с
факторизацией |
| title_full | On π-Solvable and Locally π-Solvable Groups with Factorization |
| title_fullStr | On π-Solvable and Locally π-Solvable Groups with Factorization |
| title_full_unstemmed | On π-Solvable and Locally π-Solvable Groups with Factorization |
| title_short | On π-Solvable and Locally π-Solvable Groups with Factorization |
| title_sort | on π-solvable and locally π-solvable groups with factorization |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4304 |
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