Unit groups of group algebras of groups of order 20

The group of units of group algebras of abelian groups of order 36 and $C_{3}\times A_{4}$ over any finite field

“…Most recently, Sahai and Ansari, in [1,16] completely characterized the unit groups of group algebras of group of order 16 and 20. In this paper, we will determine the structure of unit groups of group algebras of all four non-isomorphic abelian group C 36 , C 2 6 , C 2 × C 18 , C 3 × C 12 and one non abelian group C 3 × A 4 of order 36. Our notations are same as in [2,16].…”

Unit groups of group algebras of Abelian groups of order 32

“…Our problem is based on the Witt-Berman theorem [6, Ch.17, Theorem 5.3], which states that the number of non-isomorphic simple F G-modules is equal to the number of F -conjugacy classes of p-regular elements of G. Problem of finding unit groups of group algebras generated a considerable interest in recent decade and can be easily seen in [5,7,8,10,[13][14][15]. Recently in [1,12], Sahai and Ansari have characterized the unit groups of group algebras of groups of orders 16 and 20. Let G be a group of order 32, we have seven non-isomorphic abelian groups C 32 ,…”

Unit Groups of Group Algebras of Abelian Groups of order 32

“…Our problem is based on the Witt-Berman theorem [6, Ch.17, Theorem 5.3], which states that the number of non-isomorphic simple F G-modules is equal to the number of F -conjugacy classes of p-regular elements of G. Problem of finding unit groups of group algebras generated a considerable interest in recent decade and can be easily seen in [2,5,7,8,10,[13][14][15]. Recently in [1,12], Sahai and Ansari have characterized the unit groups of group algebras for the abelian groups of orders up to 20. Let G be a group of order 32, we have seven non-isomorphic abelian groups C 32 , C 16 × C 2 , C 8 ×C 4 , C 8 ×C 2 ×C 2 , C 4 ×C 4 ×C 2 , C 4 ×C 3 2 and C 5 2 .…”