Group of units of finite group algebras of groups of order 24
UDC 512.5 Let $F$ be a finite field of characteristic $p.$  The structures of the unit groups of group algebras over $F$ of the three groups $D_{24},$ $S_4$ and $SL(2, \mathbb{Z}_3)$ of order $24$  are completely described in numerous works.  &...
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| Дата: | 2023 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2023
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/6680 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512487523221504 |
|---|---|
| author | Sahai, M. Ansari, S. F. Sahai, M. Ansari, S. F. |
| author_facet | Sahai, M. Ansari, S. F. Sahai, M. Ansari, S. F. |
| author_sort | Sahai, M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-03-06T14:26:59Z |
| description | UDC 512.5
Let $F$ be a finite field of characteristic $p.$  The structures of the unit groups of group algebras over $F$ of the three groups $D_{24},$ $S_4$ and $SL(2, \mathbb{Z}_3)$ of order $24$  are completely described in numerous works.   We present the unit groups of the group algebras over $F$ for the remaining groups of order $24,$ namely, $C_{24},$ $C_{12} \times C_2,$ $C_2^3 \times C_3,$  $C_3 \rtimes C_8,$  $C_3 \rtimes Q_8,$ $D_6 \times C_4,$ $C_6 \rtimes C_4,$  $C_3 \rtimes D_8,$ $C_3 \times D_8,$  $C_3 \times Q_8,$   $A_4 \times C_2,$ and $D_{12} \times C_2.$ |
| doi_str_mv | 10.37863/umzh.v75i2.6680 |
| first_indexed | 2026-03-24T03:29:34Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-6680 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:29:34Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-66802023-03-06T14:26:59Z Group of units of finite group algebras of groups of order 24 Group of units of finite group algebras of groups of order 24 Sahai, M. Ansari, S. F. Sahai, M. Ansari, S. F. Group Algebras, Unit Groups 16S34; 20C05 UDC 512.5 Let $F$ be a finite field of characteristic $p.$  The structures of the unit groups of group algebras over $F$ of the three groups $D_{24},$ $S_4$ and $SL(2, \mathbb{Z}_3)$ of order $24$  are completely described in numerous works.   We present the unit groups of the group algebras over $F$ for the remaining groups of order $24,$ namely, $C_{24},$ $C_{12} \times C_2,$ $C_2^3 \times C_3,$  $C_3 \rtimes C_8,$  $C_3 \rtimes Q_8,$ $D_6 \times C_4,$ $C_6 \rtimes C_4,$  $C_3 \rtimes D_8,$ $C_3 \times D_8,$  $C_3 \times Q_8,$   $A_4 \times C_2,$ and $D_{12} \times C_2.$ УДК 512.5 Група одиниць скінченногрупових алгебр груп 24-го порядку  Нехай $F$ –скінченне поле характеристики $p.$  Структури груп одиниць групових алгебр над $F$ для трьох груп $D_{24},$ $S_4$ та $SL(2, \mathbb{ Z}_3)$ 24-го порядку повністю описано в багатьох роботах.  Ми наводимо групи одиниць групових алгебр над $F$ для решти груп 24-порядку, а саме $C_{24},$ $C_{12} \times C_2,$ $C_2^3 \times раз C_3,$ $C_3 \rtimes C_8,$ $C_3 \rtimes Q_8,$ $D_6 \times C_4,$ $C_6 \rtimes C_4,$ $C_3 \rtimes D_8,$ $C_3 \times D_8,$ $C_3 \times Q_8,$ $A_4 \times C_2$ та $D_{12} \times C_2.$ Institute of Mathematics, NAS of Ukraine 2023-03-02 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/6680 10.37863/umzh.v75i2.6680 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 2 (2023); 215 - 229 Український математичний журнал; Том 75 № 2 (2023); 215 - 229 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/6680/9796 Copyright (c) 2023 Meena Sahai |
| spellingShingle | Sahai, M. Ansari, S. F. Sahai, M. Ansari, S. F. Group of units of finite group algebras of groups of order 24 |
| title | Group of units of finite group algebras of groups of order 24 |
| title_alt | Group of units of finite group algebras of groups of order 24 |
| title_full | Group of units of finite group algebras of groups of order 24 |
| title_fullStr | Group of units of finite group algebras of groups of order 24 |
| title_full_unstemmed | Group of units of finite group algebras of groups of order 24 |
| title_short | Group of units of finite group algebras of groups of order 24 |
| title_sort | group of units of finite group algebras of groups of order 24 |
| topic_facet | Group Algebras Unit Groups 16S34 20C05 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/6680 |
| work_keys_str_mv | AT sahaim groupofunitsoffinitegroupalgebrasofgroupsoforder24 AT ansarisf groupofunitsoffinitegroupalgebrasofgroupsoforder24 AT sahaim groupofunitsoffinitegroupalgebrasofgroupsoforder24 AT ansarisf groupofunitsoffinitegroupalgebrasofgroupsoforder24 |