Normal complement problem over a finite field of characteristic 2

Abstract

–Let F be a finite field of characteristic 2. In this article, we have looked into the existence of normal complement of G in , where G is either the alternating group A 4 or the dihedral group of order 4m, for an odd integer . Also, we have explicitly found a normal complement of the symmetric group S 4 in over the field F containing 2 elements.