On a finite group with OS-propermutable Sylow subgroup

A Schmidt group is a non-nilpotent group whose every proper subgroup is nilpotent. A subgroup A of a group G is called OS-propermutablein G if there is a subgroup B such that \(G = NG(A)B\) $G=NG(A)B$ , where AB is a subgroup of G and A permutes with all Schmidt subgroups of B. We proved \(p\) $p$ -solubility of a group in which a Sylow \(p\) $p$ -subgroup is OS-propermutable, where \(p\geq 7\) $p\ge 7$ 7. For \(p < 7\) $p<7$ all non-Abelian composition factors of such group are listed.