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On SS-quasinormal subgroups of finite groups. (English) Zbl 1163.20011
The authors continue taking up the concept of S-quasinormality occurring in O. H. Kegel [Math. Z. 78, 205-221 (1962; Zbl 0102.26802)] and generalising it to SS-quasinormality [S. Li, Z. Shen, J. Liu and X. Liu, J. Algebra 319, No. 10, 4275-4287 (2008; Zbl 1152.20019)]. A subgroup \(H\) of a finite group \(G\) had been defined SS-quasinormal if supplemented by, \(B\) say, in \(G\) such that \(H\) permutes with every Sylow subgroup of \(B\).
A typical result is: If \(G\) is a group and all its subgroups of prime order or order 4 are SS-quasinormal in \(G\), then \(G\) is supersoluble (Theorem 3.4). The paper also provides numerous results concerning the hypercentre of a group.

MSC:
20D35 Subnormal subgroups of abstract finite groups
20D40 Products of subgroups of abstract finite groups
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D15 Finite nilpotent groups, \(p\)-groups
20E28 Maximal subgroups
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References:
[1] DOI: 10.1080/00927879808826364 · Zbl 0915.20008
[2] DOI: 10.1007/s000130050348 · Zbl 0938.20013
[3] DOI: 10.1016/S0022-4049(00)00183-3 · Zbl 1011.20019
[4] DOI: 10.1007/BF02764949 · Zbl 0689.20036
[5] DOI: 10.1007/BF00052909 · Zbl 0930.20021
[6] DOI: 10.1016/S0022-4049(96)00172-7 · Zbl 0928.20020
[7] DOI: 10.1007/BF01110184 · Zbl 0202.02303
[8] DOI: 10.1007/BF01193999 · Zbl 0553.20007
[9] DOI: 10.1007/BF01111801 · Zbl 0114.02004
[10] DOI: 10.1515/9783110870138
[11] Gorenstein D., Finite Groups (1968)
[12] Huppert B., Endliche Gruppen I (1967) · Zbl 0217.07201
[13] Huppert B., Finite Groups III (1982) · Zbl 0514.20002
[14] DOI: 10.1007/s000130050068 · Zbl 0882.20013
[15] DOI: 10.1007/BF01195169 · Zbl 0102.26802
[16] DOI: 10.1016/j.jalgebra.2008.01.030 · Zbl 1152.20019
[17] DOI: 10.1006/jabr.1998.7429 · Zbl 0910.20015
[18] DOI: 10.1007/BF01903844 · Zbl 0725.20018
[19] DOI: 10.1007/BF02761191 · Zbl 0437.20012
[20] Weinstein M., Between Nilpotent and Solvable (1982)
[21] DOI: 10.1007/BF01229714 · Zbl 0307.20012
[22] DOI: 10.1007/BF01224720 · Zbl 0348.20016
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