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On permutability of $n$-maximal subgroups with $p$-nilpotent Schmidt subgroups

V. N. Kniahina

Gomel Engineering Institute, Ministry of Extraordinary Situations of the Republic of Belarus

Abstract: A Schmidt group is a finite nonnilpotent group in which every proper subgroup is nilpotent. Fix a positive integer $n.$ Let $G$ be a solvable group. Suppose that each $n$-maximal subgroup of $G$ is permutable with every $p$-nilpotent Schmidt subgroup. We prove that if $n\in\{1,2,3\},$ then $G/F(G)$ is $p$-closed, where $F(G)$ is the Fitting subgroup of $G$.

UDC: 512.542

Received: 21.04.2016