Abstract
Let G be a group and The permutizer of H in G is
H is said to be strongly permuteral in G if
whenever
Moreover, let
is a primary element of
H is said to be strongly
-permuteral in G if
whenever
In this article, we study the structure of a group G in which every Sylow subgroup and its maximal subgroups are strongly
-permuteral or abnormal and the structure of G with self-normalizing or strongly permuteral Sylow subgroups.
Acknowledgments
The authors are indebted to the referees for valuable suggestions and very careful reading of the original manuscript.