The Structure of the Unit Group of the Group Algebra

Abstract

Abstract. Let RG denote the group ring of the group G over the ring R. Using an isomorphism between RG and a certain ring of n × n matrices in conjunction with other techniques, the structure of the unit group of the group algebra of the dihedral group of order 8 over any finite field of chracteristic 2 is determined in terms of split extensions of cyclic groups.

On the unitary units of the group algebra 𝔽2kQ16

“…The structure of U(F 2 D 8 ) were described by Sandling [20] and the structure of U(F 2 k D 8 ) further characterized by Creedon and Gildea [7], where D 8 is the dihedral group of order 8.…”

ON THE STRUCTURE OF THE UNITARY SUBGROUP OF THE GROUP ALGEBRA 𝔽2qD2n

“…In addition, if G is a finite 2-group and F is a finite field of characteristic 2, then V (FG) is a finite 2-group of order |F| |G|−1 . The structure of U(F 2 D 8 ) is given by Sandling [19] and the structure of the U(F 2 k D 8 ) is established by Creedon and Gildea [8], where D 8 is the dihedral group of order 8.…”

Unit groups of group algebras of some small groups

“…Recently there are quite a few papers which characterize the structures of unit groups of group algebras of certain small groups over finite fields (see for example [3], [5], [4], [6], [7], [9], [8], [10], [11], [15], [2], [16]). Most recently, in [2] Tang et al determined the structures of unit groups of group algebras F G of any groups of order 21 over finite fields except for the case when G is the non-abelian group of order 21 and F is a field of characteristic 3.…”