Abstract

Let \(G\) be a finite group, let \(M\) be a maximal subgroup of \(G\), and let \(\mathfrak F\) be a hereditary formation consisting of solvable groups. The metanilpotency of the \(\mathfrak F\)-residual \(G^\mathfrak F\) is established under the assumption that all subgroups maximal in \(M\) are \(\mathfrak F\)-subnormal in \(G\), and the nilpotency of \(G^\mathfrak F\) is established in the case where \(\mathfrak F\) is saturated. Properties of the group \(G\) are indicated in more detail for the formation of all solvable groups with Abelian Sylow subgroups, for the formation of all supersolvable groups, and for the formation of all groups with nilpotent commutator subgroup.

中文翻译：

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具有$$ \ mathfrak F $$的有限组-次正规子组

摘要

令\（G \）为有限群，令\（M \）为\（G \）的最大子群，令\（\ mathfrak F \）为由可解群组成的遗传结构。假设\（\ mathfrak F \）-残基\（G ^ \ mathfrak F \）的后幂是在\（M \）中最大的所有子组都是\（\ mathfrak F \）- subnormal在\（ G \），并且在\（\ mathfrak F \）饱和的情况下建立了\（G ^ \ mathfrak F \）的幂等性。组\（G \）的属性 对于形成具有Abelian Sylow子基团的所有可溶基团，形成所有超可解基团以及形成具有全能换向子基团的所有基团，将更详细地指出。