Groups with subnormal or modular Schmidt 𝑝𝑑-subgroups

Abstract

A Schmidt group is a finite non-nilpotent group such that every proper subgroup is nilpotent. In this paper, we prove that if every Schmidt subgroup of a finite group 𝐺 is subnormal or modular, then G / F ⁢ ( G ) G/F(G) is cyclic. Moreover, for a given prime 𝑝, we describe the structure of finite groups with subnormal or modular Schmidt subgroups of order divisible by 𝑝.