On unit group of finite semisimple group algebras of non-metabelian groups up to order 72
We characterize the unit group of semisimple group algebras $\mathbb{F}_qG$ of some non-metabelian groups, where $F_q$ is a field with $q=p^k$ elements for $p$ prime and a positive integer $k$. In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group $((C_3\t...
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Institute of Mathematics of the Czech Academy of Science
2021
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oai:doaj.org-article:4c9dc5adca9646f3a8bd21c129b14e3b2021-11-08T09:59:12ZOn unit group of finite semisimple group algebras of non-metabelian groups up to order 720862-79592464-713610.21136/MB.2021.0116-19https://doaj.org/article/4c9dc5adca9646f3a8bd21c129b14e3b2021-12-01T00:00:00Zhttp://mb.math.cas.cz/full/146/4/mb146_4_5.pdfhttps://doaj.org/toc/0862-7959https://doaj.org/toc/2464-7136We characterize the unit group of semisimple group algebras $\mathbb{F}_qG$ of some non-metabelian groups, where $F_q$ is a field with $q=p^k$ elements for $p$ prime and a positive integer $k$. In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group $((C_3\times C_3)\rtimes C_3)\rtimes C_2$ of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.Gaurav MittalRajendra Kumar SharmaInstitute of Mathematics of the Czech Academy of Sciencearticle unit group finite field wedderburn decompositionMathematicsQA1-939ENMathematica Bohemica, Vol 146, Iss 4, Pp 429-455 (2021) |
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| topic |
unit group finite field wedderburn decomposition Mathematics QA1-939 |
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unit group finite field wedderburn decomposition Mathematics QA1-939 Gaurav Mittal Rajendra Kumar Sharma On unit group of finite semisimple group algebras of non-metabelian groups up to order 72 |
| description |
We characterize the unit group of semisimple group algebras $\mathbb{F}_qG$ of some non-metabelian groups, where $F_q$ is a field with $q=p^k$ elements for $p$ prime and a positive integer $k$. In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group $((C_3\times C_3)\rtimes C_3)\rtimes C_2$ of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72. |
| format |
article |
| author |
Gaurav Mittal Rajendra Kumar Sharma |
| author_facet |
Gaurav Mittal Rajendra Kumar Sharma |
| author_sort |
Gaurav Mittal |
| title |
On unit group of finite semisimple group algebras of non-metabelian groups up to order 72 |
| title_short |
On unit group of finite semisimple group algebras of non-metabelian groups up to order 72 |
| title_full |
On unit group of finite semisimple group algebras of non-metabelian groups up to order 72 |
| title_fullStr |
On unit group of finite semisimple group algebras of non-metabelian groups up to order 72 |
| title_full_unstemmed |
On unit group of finite semisimple group algebras of non-metabelian groups up to order 72 |
| title_sort |
on unit group of finite semisimple group algebras of non-metabelian groups up to order 72 |
| publisher |
Institute of Mathematics of the Czech Academy of Science |
| publishDate |
2021 |
| url |
https://doaj.org/article/4c9dc5adca9646f3a8bd21c129b14e3b |
| work_keys_str_mv |
AT gauravmittal onunitgroupoffinitesemisimplegroupalgebrasofnonmetabeliangroupsuptoorder72 AT rajendrakumarsharma onunitgroupoffinitesemisimplegroupalgebrasofnonmetabeliangroupsuptoorder72 |
| _version_ |
1718442710820454400 |