The unit groups of semisimple group algebras of some non-metabelian groups of order $144$

IF 0.3 Q4 MATHEMATICS Mathematica Bohemica Pub Date : 2022-12-19 DOI:10.21136/mb.2022.0067-22
Gaurav Mittal, R. Sharma
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引用次数: 0

Abstract

. We consider all the non-metabelian groups G of order 144 that have exponent either 36 or 72 and deduce the unit group U ( F q G ) of semisimple group algebra F q G . Here, q denotes the power of a prime, i.e., q = p r for p prime and a positive integer r . Up to isomorphism, there are 6 groups of order 144 that have exponent either 36 or 72. Additionally, we also discuss how to simply obtain the unit groups of the semisimple group algebras of those non-metabelian groups of order 144 that are a direct product of two nontrivial groups. In all, this paper covers the unit groups of semisimple group algebras of 17 non-metabelian groups.
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一类$144阶非变倍群的半单群代数的单位群$
我们考虑指数为36或72的所有144阶的非偏贝群G,并推导出半单群代数FqG的单位群U(FqG)。这里,q表示素数的幂,即,对于p素数和正整数r,q=pr。直到同构,有6个144阶的群的指数为36或72。此外,我们还讨论了如何简单地获得作为两个非平凡群的直积的144阶非偏李群的半单群代数的单位群。总之,本文覆盖了17个非变倍群的半单群代数的单位群。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Mathematica Bohemica
Mathematica Bohemica MATHEMATICS-
CiteScore
1.10
自引率
0.00%
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0
审稿时长
52 weeks
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