Structure of unit group of FpnD60

Abstract

Let [Formula: see text] be a finite field with characteristic [Formula: see text] having [Formula: see text] elements and [Formula: see text] be the dihedral group of order [Formula: see text]. In this paper, we have obtained the structure of unit groups of group algebra [Formula: see text], for any prime [Formula: see text].

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

“…For other basic details see [13]. In recent years, we have seen a lot of papers that characterize the structure of unit groups of group algebras and can be easily found in [2,5,6,12,14,17,18,19,20].…”

“…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

“…An element g ∈ G is called p-regular if (p, o(g)) = 1, where CharF = p > 0. Notation used in this paper are same as in [2]. 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].…”

Unit Groups of Group Algebras of Abelian Groups of order 32

“…This defines an equivalence relation, so we have a partitions of the p-regular elements of G into p-regular, F -conjugacy classes. 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.…”