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Let  p  and  q  be odd primes such thatLet  F  be the field with  p  elements andbe a group, where  A  is an abelian group of orderIn this article, we prove that ifthen  G  does not have a normal complement inFurther, for any integerwe prove that if  F  is a finite field such thatthenanddo not have a normal complement inandrespectively.

On the normal complement problem in modular and semisimple group algebras