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\(\mathfrak F\)-groups and Hall \(s\)-semiembedded subgroups. (English) Zbl 1369.20020

Summary: Let \(G\) be a finite group. A subgroup \(H\) of \(G\) is said to be a Hall \(s\)-semiembedded subgroup of \(G\) if \(H\) is a Hall subgroup of \(\langle H,P \rangle\) for any \(P \in \mathrm {Syl}_p(G)\), where \((p,|H|)=1\). In this paper, we investigate the influence of Hall \(s\)-semiembedded subgroups on the structure of the finite group \(G\). Some new results about \(G\) to be a \(\mathfrak F\)-group are obtained, where is a saturated formation.

MSC:

20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D40 Products of subgroups of abstract finite groups
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
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References:

[1] Ballester-Bolinches, A. and Pedraza-Aguilera, M. C., On minimal subgroups of finite groups, Acta Math. Hungar.73(4) (1996) 335-342. · Zbl 0930.20021
[2] Guo, W., The Theory of Classes of Groups (Science Press-Kluwer Academic Publishers, 2000).
[3] Guo, W., The influence of minimal subgroups on the structure of finite groups, Southeast Asia Bull. Math.22 (1998) 287-290. · Zbl 0937.20008
[4] Huppert, B., Endliche Gruppen 1 (Springer, New York, 1967). · Zbl 0217.07201
[5] Huppert, B. and Blackburn, N., Finite Groups III (Springer, Berlin, 1982). · Zbl 0514.20002
[6] Isaacs, I. M., Semipermutable \(\pi \)-subgroups, Arch. Math.102 (2014) 1-6. · Zbl 1297.20018
[7] Li, Y., He, X. and Wang, Y., On \(s\)-semipermutable subgroups of finite groups, Acta Math. Sin. (Engl. Ser.)26(11) (2010) 2215-2222. · Zbl 1209.20018
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