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 ðn 4Þ in their corresponding unit groups UðFSnÞ and UðFAnÞ:
Moreover, if F is a finite field of characteristic 3, then A4 does not have normal complement in the unit group UðFA4Þ:
