THE QUASI-SUPERFLUOUS ELEMENTS OF A GROUP
An element xof a group Gis quasi-superfluous in G, if ?permutes with every maximal subgroup of G. The set ?of allquasi-superfluous elements of G (a set which contains the Frattini subgroup ?is known to be a nilpotent characteristic subgroup in every finite group. We establish some sufficient conditions for the subgroup property of
Frattini subgroup, a quasi-superfluous element, hyper-radical groups.
