On unit group of finite semisimple group algebras of non-metabelian groups up to order 72
We characterize the unit group of semisimple group algebras of some non-metabelian groups, where is a field with elements for prime and a positive integer . In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group 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.