On \(S\)-quasinormally embedded subgroups of finite groups. (English) Zbl 1011.20019

This paper considers the consequences of a finite group \(G\) having special families of subgroups that are \(S\)-quasinormally embedded in \(G\). Sample result: Theorem 3.1. Let \(G\) be a finite group and let \(p\) be the smallest prime dividing \(|G|\). Then the following are equivalent: (a) \(G\) is \(p\)-nilpotent; (b) The maximal subgroups of the Sylow \(p\)-subgroups of \(G\) are \(S\)-quasinormally embedded in \(G\).


20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D30 Series and lattices of subgroups
20D40 Products of subgroups of abstract finite groups
Full Text: DOI


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