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 V(FG), where G is either the alternating group A4 or the dihedral group D4m of order 4m, for an odd integer m ≥ 3. Also, we have explicitly found a normal complement of the symmetric group S4 in V(FS4) over the field F containing 2 elements.