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

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.