Finite Groups with X-Quasipermutable Sylow Subgroups

摘要

Let H a parts per thousand currency sign E and X be subgroups of a finite group G. Then we say that H is X-quasipermutable (XS -quasipermutable, respectively) in E provided that G has a subgroup B such that E = N (E) (H)B and H is X-permutable with B and with all subgroups (with all Sylow subgroups, respectively) V of B such that (|H|, |V |) = 1. We analyze the influence of X-quasipermutable and X (S) -quasipermutable subgroups on the structure of G. In particular, it is proved that if every Sylow subgroup P of G is F(G) -quasipermutable in its normal closure P (G) in G, then G is supersoluble.