On the nilpotency class of a multiplicative group of a modular group algebra of a dihedral 2-group
It is proved that the wreath product of a second-order group and the commutant of a dihedral group is imbedded into a multiplicative group of a modular group algebra of a dihedral group of order 2 n . This implies that the nilpotency class of the multiplicative group is equal to 2 n−2, i.e., to the...
Збережено в:
| Дата: | 1995 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1995
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5380 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511611235598336 |
|---|---|
| author | Konovalov, A. B. Коновалов, А. Б. Коновалов, А. Б. |
| author_facet | Konovalov, A. B. Коновалов, А. Б. Коновалов, А. Б. |
| author_sort | Konovalov, A. B. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T08:58:17Z |
| description | It is proved that the wreath product of a second-order group and the commutant of a dihedral group is imbedded into a multiplicative group of a modular group algebra of a dihedral group of order 2 n . This implies that the nilpotency class of the multiplicative group is equal to 2 n−2, i.e., to the order of the commutant of the dihedral group. |
| first_indexed | 2026-03-24T03:15:38Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5380 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:15:38Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/4c/30fe0f8dbad2f9ce5db826d99ec0624c.pdf |
| spelling | umjimathkievua-article-53802020-03-19T08:58:17Z On the nilpotency class of a multiplicative group of a modular group algebra of a dihedral 2-group О классе нильпотентности мультипликативной группы модулярной групповой алгебры 2-группы диэдра Konovalov, A. B. Коновалов, А. Б. Коновалов, А. Б. It is proved that the wreath product of a second-order group and the commutant of a dihedral group is imbedded into a multiplicative group of a modular group algebra of a dihedral group of order 2 n . This implies that the nilpotency class of the multiplicative group is equal to 2 n−2, i.e., to the order of the commutant of the dihedral group. Доведено, що в мультиплікативну групу модулярної групової алгебри групи діедра порядку $2^{n}$ вкладено вінцевий добуток групи порядку 2 та комутанта групи діедра. З цього виходить, що клас нільгіотентності мультиплікативної групи дорівнює $2^{n−2}$, тобто порядку комутанта групи діедра. Institute of Mathematics, NAS of Ukraine 1995-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5380 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 1 (1995); 39–45 Український математичний журнал; Том 47 № 1 (1995); 39–45 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5380/7451 https://umj.imath.kiev.ua/index.php/umj/article/view/5380/7452 Copyright (c) 1995 Konovalov A. B. |
| spellingShingle | Konovalov, A. B. Коновалов, А. Б. Коновалов, А. Б. On the nilpotency class of a multiplicative group of a modular group algebra of a dihedral 2-group |
| title | On the nilpotency class of a multiplicative group of a modular group algebra of a dihedral 2-group |
| title_alt | О классе нильпотентности мультипликативной группы модулярной групповой алгебры 2-группы диэдра |
| title_full | On the nilpotency class of a multiplicative group of a modular group algebra of a dihedral 2-group |
| title_fullStr | On the nilpotency class of a multiplicative group of a modular group algebra of a dihedral 2-group |
| title_full_unstemmed | On the nilpotency class of a multiplicative group of a modular group algebra of a dihedral 2-group |
| title_short | On the nilpotency class of a multiplicative group of a modular group algebra of a dihedral 2-group |
| title_sort | on the nilpotency class of a multiplicative group of a modular group algebra of a dihedral 2-group |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5380 |
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