Groups satisfying the condition of weak minimality for subgroups of derived length two
We consider non-Abelian solvable and radical groups that satisfy the condition of weak minimality for subgroups of derived length two. We show that these groups are minimax groups. This is not true for locally solvable groups. We give an example of a group of derived length three that satisfies the...
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| Дата: | 1994 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1994
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5636 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511864937512960 |
|---|---|
| author | Onishchuk, V. A. Онищук, В. А. |
| author_facet | Onishchuk, V. A. Онищук, В. А. |
| author_sort | Onishchuk, V. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:14:58Z |
| description | We consider non-Abelian solvable and radical groups that satisfy the condition of weak minimality for subgroups of derived length two. We show that these groups are minimax groups. This is not true for locally solvable groups. We give an example of a group of derived length three that satisfies the condition of weak minimality for the indicated subgroups but is not a minimax group. |
| first_indexed | 2026-03-24T03:19:40Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5636 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:19:40Z |
| publishDate | 1994 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/a1/23ae7f65561dcef5ea97bea9dc0451a1.pdf |
| spelling | umjimathkievua-article-56362020-03-19T09:14:58Z Groups satisfying the condition of weak minimality for subgroups of derived length two Группы, удовлетворяющие слабому условию минимальности для двуступепно разрешимых подгрупп Onishchuk, V. A. Онищук, В. А. We consider non-Abelian solvable and radical groups that satisfy the condition of weak minimality for subgroups of derived length two. We show that these groups are minimax groups. This is not true for locally solvable groups. We give an example of a group of derived length three that satisfies the condition of weak minimality for the indicated subgroups but is not a minimax group. Non-Abelian solvable and radical groups satisfying the weak minimality condition for solvable subgroups of derived lentgh two are studied. It is shown that such groups are minimax ones. For locally solvable groups, an analogous statement is not true. We also give an example of a solvable group of derived length three that satisfies the weak minimality condition for subgroups of derived length three but is not a minimax group. Institute of Mathematics, NAS of Ukraine 1994-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5636 Ukrains’kyi Matematychnyi Zhurnal; Vol. 46 No. 9 (1994); 1203–1207 Український математичний журнал; Том 46 № 9 (1994); 1203–1207 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5636/7957 https://umj.imath.kiev.ua/index.php/umj/article/view/5636/7958 Copyright (c) 1994 Onishchuk V. A. |
| spellingShingle | Onishchuk, V. A. Онищук, В. А. Groups satisfying the condition of weak minimality for subgroups of derived length two |
| title | Groups satisfying the condition of weak minimality for subgroups of derived length two |
| title_alt | Группы, удовлетворяющие слабому условию минимальности для двуступепно разрешимых подгрупп |
| title_full | Groups satisfying the condition of weak minimality for subgroups of derived length two |
| title_fullStr | Groups satisfying the condition of weak minimality for subgroups of derived length two |
| title_full_unstemmed | Groups satisfying the condition of weak minimality for subgroups of derived length two |
| title_short | Groups satisfying the condition of weak minimality for subgroups of derived length two |
| title_sort | groups satisfying the condition of weak minimality for subgroups of derived length two |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5636 |
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