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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2021-12-01
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| Series: | Mathematica Bohemica |
| Subjects: | |
| Online Access: | http://mb.math.cas.cz/full/146/4/mb146_4_5.pdf |
| Summary: | 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. |
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| ISSN: | 0862-7959 2464-7136 |