On unit group of finite semisimple group algebras of non-metabelian groups up to order 72

Abstract

We characterize the unit group of semisimple group algebras FqG of some non-metabelian groups, where Fq is a field with q = p k elements for p prime and a positive integer k. In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group ((C3 × C3)⋊ C3)⋊ C2 of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.