Abstract:
Let Sn be the symmetric group and An be the alternating group on n symbols. In this article, we have proved that if F is a finite field of characteristic p > n, then there does not exist a normal complement of Sn (n is even) and An (Formula presented.) in their corresponding unit groups (Formula presented.) and (Formula presented.) Moreover, if F is a finite field of characteristic 3, then A 4 does not have normal complement in the unit group (Formula presented.)
