Groups with elementary abelian commutant of at most $p^2$th order
We obtain a representation of nilpotent groups with a commutant of the type $(p)$ or $(p, p)$ that has the form of a product of two normal subgroups. One of these subgroups is constructively described as a Chernikov $p$-group of rank 1 or 2, and the other subgroup has a certain standard form. We als...
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| Datum: | 1998 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1998
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4923 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511108920508416 |
|---|---|
| author | Mazurok, О. O. Мазурок, О. О. |
| author_facet | Mazurok, О. O. Мазурок, О. О. |
| author_sort | Mazurok, О. O. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:17:16Z |
| description | We obtain a representation of nilpotent groups with a commutant of the type $(p)$ or $(p, p)$ that has the form of a product of two normal subgroups. One of these subgroups is constructively described as a Chernikov $p$-group of rank 1 or 2, and the other subgroup has a certain standard form. We also obtain a representation of nonnilpotent groups with a commutant of the type $(p)$ or $(p, p)$ in the form of a semidirect product of a normal subgroup of the type $(p)$ or $(p, p)$ and a nilpotent subgroup with a commutant of order $p$ or 1. |
| first_indexed | 2026-03-24T03:07:39Z |
| format | Article |
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| id | umjimathkievua-article-4923 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:07:39Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b7/1166417a7ac51cf9b562582c6fb1f5b7.pdf |
| spelling | umjimathkievua-article-49232020-03-18T21:17:16Z Groups with elementary abelian commutant of at most $p^2$th order Групи з елементарним абелевим комутантом порядку не більше ніж $p^2$ Mazurok, О. O. Мазурок, О. О. We obtain a representation of nilpotent groups with a commutant of the type $(p)$ or $(p, p)$ that has the form of a product of two normal subgroups. One of these subgroups is constructively described as a Chernikov $p$-group of rank 1 or 2, and the other subgroup has a certain standard form. We also obtain a representation of nonnilpotent groups with a commutant of the type $(p)$ or $(p, p)$ in the form of a semidirect product of a normal subgroup of the type $(p)$ or $(p, p)$ and a nilpotent subgroup with a commutant of order $p$ or 1. Отримано зображення нільпотентиих груп з комутантом типу $(p)$ чи $(p, p)$ у вигляді добутку двох нормальних підгруп, одна з яких конструктивно описана як черпіковська $p$-група рангу 1 або 2, а друга має певний стандартизований вигляд, і непільпотеитних груп з комутантом типу $(p)$ чи $(p, p)$ — у вигляді напівпрямого добутку нормальної підгрупи типу $(p)$ чи $(p, p)$ і деякої нільпотептної підгрупи з комутантом порядку $p$ або 1. Institute of Mathematics, NAS of Ukraine 1998-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4923 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 4 (1998); 534-539 Український математичний журнал; Том 50 № 4 (1998); 534-539 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4923/6545 https://umj.imath.kiev.ua/index.php/umj/article/view/4923/6546 Copyright (c) 1998 Mazurok О. O. |
| spellingShingle | Mazurok, О. O. Мазурок, О. О. Groups with elementary abelian commutant of at most $p^2$th order |
| title | Groups with elementary abelian commutant of at most $p^2$th order |
| title_alt | Групи з елементарним абелевим комутантом порядку не більше ніж $p^2$ |
| title_full | Groups with elementary abelian commutant of at most $p^2$th order |
| title_fullStr | Groups with elementary abelian commutant of at most $p^2$th order |
| title_full_unstemmed | Groups with elementary abelian commutant of at most $p^2$th order |
| title_short | Groups with elementary abelian commutant of at most $p^2$th order |
| title_sort | groups with elementary abelian commutant of at most $p^2$th order |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4923 |
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