Abstract:

A subgroup of a group G is said to be π-quasinormal in G if it permutes with every Sylow subgroup of G, which was firstly posed by Kegel. Since then,
a long series of papers deal with π-quasinormality well located in G. In this paper we localize the above conditions in the G-normalizer of Sylow subgroups of the group G.

Key words: Finite groups, Maximal subgroups, π-quasinormal, Saturated formations