THE UNIT GROUPS OF SEMISIMPLE GROUP ALGEBRAS OF SOME NON-METABELIAN GROUPS OF ORDER 144

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.