Normal complement problem over a finite field of characteristic 2.

–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 (F G) , where G is either the alternating group A4 or the dihedral group D 4 m of order 4m, for an odd integer m ≥ 3 . Also, we have explicitly found a normal complement of the symmetric group S4 in V (F S 4) over the field F containing 2 elements. [ABSTRACT FROM AUTHOR]