On unit group of finite semisimple group algebras of non-metabelian groups of order 108

  • Gaurav Mittal
  • Rajendra Sharma IIT Delhi
Keywords: Unit group, Finite field, Wedderburn decomposition


In this paper, we characterize the unit groups of semisimple group algebras $\mathbb{F}_qG$ of non-metabelian groups of order $108$, where $F_q$ is a field with $q=p^k$ elements for some prime $p > 3$ and positive integer $k$. Up to isomorphism, there are $45$ groups of order $108$ but only $4$ of them are non-metabelian. We consider all the non-metabelian groups of order $108$ and find the Wedderburn decomposition of their semisimple group algebras. And as a by-product obtain the unit groups.


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