Abstract

There are five non-isomorphic groups of order 18. Of these two groups are abelian and the rest are non-abelian. In this article, we give the structures of the unit groups of the finite group algebras of all groups of order 18, i.e., $U(F{C}_{18}),U(F{D}_{18}),U(F(D_6\times C_3)),U(F(C_3^2⋊C_2))$ and $U(F(C_6\times C_3)),$ where F is a finite field.

中文翻译：

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18阶群的群代数的单位群

摘要

有五个 18 阶非同构群。这两个群是阿贝尔群，其余的群是非阿贝尔群。在本文中，我们给出所有18阶群的有限群代数的单位群的结构，即，$你(F{C}_{18}),你(F{D}_{18}),你(F(D_6\times C_3)),你(F(C_3^2⋊C_2))$ 和 $你(F(C_6\times C_3)),$其中F是有限域。