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On unit group of finite semisimple group algebras of non-metabelian groups up to order 72
Mathematica Bohemica, Tome 146 (2021) no. 4, pp. 429-455 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/MB.2021.0116-19
Classification : 16U60, 20C05
Keywords: unit group; finite field; Wedderburn decomposition 
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     journal = {Mathematica Bohemica},
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     year = {2021},
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Mittal, Gaurav; Sharma, Rajendra Kumar. On unit group of finite semisimple group algebras of non-metabelian groups up to order 72. Mathematica Bohemica, Tome 146 (2021) no. 4, pp. 429-455. doi: 10.21136/MB.2021.0116-19

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