Coleman automorphisms of permutational wreath products II

ABSTRACT

Let K be an arbitrary permutation group on a finite set Ω. Let G = H≀K be the corresponding permutational wreath product of a group H by K. It is proved that every Coleman automorphism of G is inner whenever H is either an almost simple group or a p-constrained group with $O_{p^{\prime }}\left(H\right)=1$ for some prime p. In particular, the normalizer conjecture holds for such groups G. Other positive results regarding the normalizer conjecture are also obtained. Our results extend some known ones.

KEYWORDS:

• Coleman automorphism
• permutational wreath product
• the normalizer conjecture

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D45
• 20E22
• 20C05

Acknowledgments

The author is grateful to the anonymous referee, who made many helpful comments and suggestions that greatly improved the quality of the paper.