Abstract
Let p and q be odd primes such that Let F be the field with p elements and
be a group, where A is an abelian group of order
In this article, we prove that if
then G does not have a normal complement in
Further, for any integer
we prove that if F is a finite field such that
then
and
do not have a normal complement in
and
respectively.
Acknowledgement
The author would like to thank the referee for the valuable comments and suggestions which improved the presentation of the article.