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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 \(G\).

MSC:

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
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References:

[1] Asaad, M., On maximal subgroups of Sylow subgroups of finite groups, Comm. in algebra, 26, 3647-3652, (1998) · Zbl 0915.20008
[2] Ballester-Bolinches, A.; Pedraza-Aguilera, M.C., Sufficient conditions for supersolvability of finite groups, J. pure appl. algebra, 127, 113-118, (1998) · Zbl 0928.20020
[3] Deskins, W.E., On quasinormal subgroups of finite groups, Math. Z., 82, 125-132, (1963) · Zbl 0114.02004
[4] Doerk, K.; Hawkes, T., Finite solvable groups, (1992), Walter de Gruyter Berlin
[5] Gorenstein, D., Finite groups, (1968), Harper & Row New York · Zbl 0185.05701
[6] Huppert, B., Endliche gruppen I, (1979), Springer Berlin · Zbl 0412.20002
[7] Kegel, O.H., Sylow-gruppen und subnormalteiler endlicher gruppen, Math. Z., 78, 205-221, (1962) · Zbl 0102.26802
[8] Srinivasan, S., Two sufficient conditions for supersolvability of finite groups, Israel J. math, 35, 210-214, (1980) · Zbl 0437.20012
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