Group of units of finite group algebras of groups of order 24

Abstract

UDC 512.5 Let F be a finite field of characteristic p . The structures of the unit groups of group algebras over F of the three groups D 24 , S 4 and S L ( 2 , ℤ 3 ) of order 24 are completely described in numerous works. We present the unit groups of the group algebras over F for the remaining groups of order 24 , namely, C 24 , C 12 × C 2 , C 2 3 × C 3 , C 3 ⋊ C 8 , C 3 ⋊ Q 8 , D 6 × C 4 , C 6 ⋊ C 4 , C 3 ⋊ D 8 , C 3 × D 8 , C 3 × Q 8 , A 4 × C 2 , and D 12 × C 2 .