On the crossing of maximal subgroups of finite groups
UDC 517.542 We establish the structure of normghal subgroups in $\theta$-Frattini extensions, where $\theta$ is a subgroup functor. For a local Fitting structure $\frak F$ containing all nilpotent groups, it is shown that, in a solvable group, the crossing of $\frak F$-abnormal maximal $\theta$-sub...
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| Datum: | 2026 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1528 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860507322318585856 |
|---|---|
| author | Borodich, R. V. Бородич, Р. В. Бородич, Р. В. |
| author_facet | Borodich, R. V. Бородич, Р. В. Бородич, Р. В. |
| author_sort | Borodich, R. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-02-09T14:27:57Z |
| description | UDC 517.542
We establish the structure of normghal subgroups in $\theta$-Frattini
extensions, where $\theta$ is a subgroup functor.
For a local Fitting structure $\frak F$ containing all nilpotent groups, it is shown that, in a solvable group, the crossing of $\frak F$-abnormal maximal $\theta$-subgroups not containing $\frak F$-radicals and not belonging to $\frak F$ coincides with the crossing of $\frak F$-abnormal maximal $\theta$-subgroups and belongs to the structure of $\frak F.$ |
| doi_str_mv | 10.3842/umzh.v71i11.1528 |
| first_indexed | 2026-03-24T02:07:28Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-1528 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T02:07:28Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/30/7b015270eda2318a0b80025443253430 |
| spelling | umjimathkievua-article-15282026-02-09T14:27:57Z On the crossing of maximal subgroups of finite groups О пересечении максимальных подгрупп конечных групп Borodich, R. V. Бородич, Р. В. Бородич, Р. В. UDC 517.542 We establish the structure of normghal subgroups in $\theta$-Frattini extensions, where $\theta$ is a subgroup functor. For a local Fitting structure $\frak F$ containing all nilpotent groups, it is shown that, in a solvable group, the crossing of $\frak F$-abnormal maximal $\theta$-subgroups not containing $\frak F$-radicals and not belonging to $\frak F$ coincides with the crossing of $\frak F$-abnormal maximal $\theta$-subgroups and belongs to the structure of $\frak F.$ УДК 517.542 Встановлено будову нормальних підгруп у $\theta$-фраттінієвих розширеннях, де $\theta$ - пiдгруповий функтор. Для локальної формацiї Фіттінга $\frak F,$ що мiстить усi нільпотентні групи, показано, що у розв'язуваній групi перетин $\frak F$-абнормальних максимальних $\theta$-підгруп, що не мiстять $\frak F$-радикала i не належать $\frak F,$ збігається з перетином $\frak F$-абнормальних максимальних $\theta$-підгруп i належить формацiї $\frak F.$ Institute of Mathematics, NAS of Ukraine 2026-02-09 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/1528 10.3842/umzh.v71i11.1528 Ukrains’kyi Matematychnyi Zhurnal; Vol. 71 No. 11 (2019); 1455-1465 Український математичний журнал; Том 71 № 11 (2019); 1455-1465 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/1528/510 Copyright (c) 2019 Borodich R. V. |
| spellingShingle | Borodich, R. V. Бородич, Р. В. Бородич, Р. В. On the crossing of maximal subgroups of finite groups |
| title | On the crossing of maximal subgroups of finite groups |
| title_alt | О пересечении максимальных подгрупп конечных групп |
| title_full | On the crossing of maximal subgroups of finite groups |
| title_fullStr | On the crossing of maximal subgroups of finite groups |
| title_full_unstemmed | On the crossing of maximal subgroups of finite groups |
| title_short | On the crossing of maximal subgroups of finite groups |
| title_sort | on the crossing of maximal subgroups of finite groups |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/1528 |
| work_keys_str_mv | AT borodichrv onthecrossingofmaximalsubgroupsoffinitegroups AT borodičrv onthecrossingofmaximalsubgroupsoffinitegroups AT borodičrv onthecrossingofmaximalsubgroupsoffinitegroups AT borodichrv operesečeniimaksimalʹnyhpodgruppkonečnyhgrupp AT borodičrv operesečeniimaksimalʹnyhpodgruppkonečnyhgrupp AT borodičrv operesečeniimaksimalʹnyhpodgruppkonečnyhgrupp |