Groups with subnormal or modular Schmidt \(pd\)-subgroups (Q6611932)

A finite group \(G\) is called a Schmidt group if \(G\) is a non-nilpotent group and every proper subgroup of \(G\) is nilpotent.\N\NIn the paper under review, the authors prove that if every Schmidt subgroup of a finite group \(G\) is subnormal or modular, then \(G/F(G)\) is cyclic. This provides a generalization of a theorem by \textit{V. A. Vedernikov} [Algebra Logika 46, No. 6, 669--687 (2007; Zbl 1155.20304); translation in Algebra Logic 46, No. 6, 363--372 (2007)]. Moreover, for a given prime \(p\), they describe the structure of finite groups with subnormal or modular Schmidt subgroups of order divisible by \(p\).