A criterion for the existence of nilpotent hall π-subgroups
Let [Formula: see text] be a nontrivial normal subgroup of [Formula: see text] and [Formula: see text]. In this paper, we show that if [Formula: see text] and for every [Formula: see text]-element [Formula: see text] with [Formula: see text], [Formula: see text], for some integer [Formula: see text], then [Formula: see text] has nilpotent Hall [Formula: see text]-subgroups. Further, we show that if [Formula: see text], then [Formula: see text] has abelian Hall [Formula: see text]-subgroups.