The unit group of the group algebra $\mathbb{F}_{q}(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$
UDC 512.5 Let $p$ be a prime, $\mathbb{F}_q$ be a finite field with $q=p^n$ elements, and $\mathbb{Z}_9\rtimes\mathbb{Z}_3$ be the  semidirect product of the groups  $\mathbb{Z}_9 $ and $\mathbb{Z}_3$. The unit group $\mathcal{U}(\mathbb{F}_q(\mathbb{Z}_9\rtime...
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| Date: | 2024 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2024
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7500 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512676772315136 |
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| author | Sharma, R. K. Kumar, Yogesh Mishra, D. C. Sharma, R. K. Kumar, Yogesh Mishra, D. C. |
| author_facet | Sharma, R. K. Kumar, Yogesh Mishra, D. C. Sharma, R. K. Kumar, Yogesh Mishra, D. C. |
| author_sort | Sharma, R. K. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-08-10T06:39:10Z |
| description | UDC 512.5
Let $p$ be a prime, $\mathbb{F}_q$ be a finite field with $q=p^n$ elements, and $\mathbb{Z}_9\rtimes\mathbb{Z}_3$ be the  semidirect product of the groups  $\mathbb{Z}_9 $ and $\mathbb{Z}_3$. The unit group $\mathcal{U}(\mathbb{F}_q(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$ of  the group algebra  $\mathbb{F}_q(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$ is  completely characterized. |
| doi_str_mv | 10.3842/umzh.v76i7.7500 |
| first_indexed | 2026-03-24T03:32:35Z |
| format | Article |
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| id | umjimathkievua-article-7500 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:35Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-75002024-08-10T06:39:10Z The unit group of the group algebra $\mathbb{F}_{q}(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$ The unit group of the group algebra $\mathbb{F}_{q}(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$ Sharma, R. K. Kumar, Yogesh Mishra, D. C. Sharma, R. K. Kumar, Yogesh Mishra, D. C. Group algebra, Wedderburn Decomposition, Unit Group. Mathematics Algebra UDC 512.5 Let $p$ be a prime, $\mathbb{F}_q$ be a finite field with $q=p^n$ elements, and $\mathbb{Z}_9\rtimes\mathbb{Z}_3$ be the  semidirect product of the groups  $\mathbb{Z}_9 $ and $\mathbb{Z}_3$. The unit group $\mathcal{U}(\mathbb{F}_q(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$ of  the group algebra  $\mathbb{F}_q(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$ is  completely characterized. УДК 512.5 Група одиниць групової алгебри $\mathbb{F}_{q}(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$  Нехай $p$ – просте число, $\mathbb{F}_q$ – скінченне поле з $q=p^n$ елементами, а $\mathbb{Z}_9\rtimes\mathbb{Z}_3$ --- напівпрямий добуток груп $\mathbb{Z}_9 $ і $\mathbb{Z}_3$. Наведено повну характеризацію групи одиниць $\mathcal{U}(\mathbb{F}_q(\mathbb{Z}_9\rtimes\mathbb{Z}_3))$ групової алгебри $\mathbb{F}_q(\mathbb{ Z}_9\rtimes\mathbb{Z}_3).$  Institute of Mathematics, NAS of Ukraine 2024-08-04 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7500 10.3842/umzh.v76i7.7500 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 7 (2024); 1086 - 1092 Український математичний журнал; Том 76 № 7 (2024); 1086 - 1092 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7500/10062 Copyright (c) 2024 Yogesh Kumar Yogesh Kumar |
| spellingShingle | Sharma, R. K. Kumar, Yogesh Mishra, D. C. Sharma, R. K. Kumar, Yogesh Mishra, D. C. The unit group of the group algebra $\mathbb{F}_{q}(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$ |
| title | The unit group of the group algebra $\mathbb{F}_{q}(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$ |
| title_alt | The unit group of the group algebra $\mathbb{F}_{q}(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$ |
| title_full | The unit group of the group algebra $\mathbb{F}_{q}(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$ |
| title_fullStr | The unit group of the group algebra $\mathbb{F}_{q}(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$ |
| title_full_unstemmed | The unit group of the group algebra $\mathbb{F}_{q}(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$ |
| title_short | The unit group of the group algebra $\mathbb{F}_{q}(\mathbb{Z}_9\rtimes\mathbb{Z}_3)$ |
| title_sort | unit group of the group algebra $\mathbb{f}_{q}(\mathbb{z}_9\rtimes\mathbb{z}_3)$ |
| topic_facet | Group algebra Wedderburn Decomposition Unit Group. Mathematics Algebra |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7500 |
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