Weakly s-semipermutable subgroups of finite groups

Yong Xu; Xianhua Li

doi:10.1007/s11464-010-0081-x

Front. Math. China ›› 2010, Vol. 6 ›› Issue (1) : 161 -175. DOI: 10.1007/s11464-010-0081-x

Research Article

RESEARCH ARTICLE

Weakly s-semipermutable subgroups of finite groups

Yong Xu ¹
, Xianhua Li ¹^,^b

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Abstract

In this paper, we introduce the concept of weakly s-semipermutable subgroups. Let G be a finite group. Using the condition that the minimal subgroups or subgroups of order p ² of a given Sylow p-subgroup of G are weakly s-semipermutable in G, we give a criterion for p-nilpotency of G and get some results about formation.

Keywords

weakly s-semipermutable subgroup / p-nilpotency / formation

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Yong Xu, Xianhua Li. Weakly s-semipermutable subgroups of finite groups. Front. Math. China, 2010, 6(1): 161-175 DOI:10.1007/s11464-010-0081-x

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References

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[1]	Ballester-Bolinches A. ℋ-normalizers and local definitions of saturated formations of finite groups. Israel J Math, 1989, 67, 312-326

[2]	Ballester-Bolinches A., Pedraza-Aguilera M. C. On minimal subgroups of finite groups. Acta Math Hungar, 1996, 73, 335-342

[3]	Chen Z. Inner Outer Σ-Group and Minimal Non Σ-Group, 1988, Chongqing: Southeast Normal University Press.

[4]	Chen Z. On a theorem of Srinivasan. J of Southwest Normal Univ (Nat Sci), 1987, 12 1 1-4

[5]	David M. B. The subgroups of PSL(3, q) for odd q. Trans Amer Math Soc, 1967, 127, 150-178

[6]	Doerk K., Hawkes T. Finite Solvable Groups, 1992, Berlin: Walter de Gruyter.

[7]	Guo W. The Theory of Classes of Groups, 2000, Beijing, New York: Science Press-Kluwer Academic Publishers.

[8]	Guo X., Shum K. P. Cover-avoidance properties and the structure of finite groups. J Pure Appl Algebra, 2003, 181, 297-308

[9]	Huppert B. Endliche Gruppen I, 1967, New York: Springer.

[10]	Huppert B., Blackburn N. Finite Groups III, 1982, Berlin-New York: Springer-Verlag.

[11]	Kegel O. H. Sylow-Gruppen and Subnormalteiler endlicher Gruppen. Math Z, 1962, 78, 205-211

[12]	Li X., Yang Y. Semi CAP-subgroups and the structure of finite groups. Acta Math Sinica, 2008, 51 6 1181-1187

[13]	Li Y., Wang Y., Wei H. On p-nilpotency of finite groups with some subgroups π-quasinormally embedded. Acta Math Hungar, 2005, 108 4 283-298

[14]	Skiba A. N. On weakly s-permutable subgroups of finite groups. J Algebra, 2007, 315 1 192-209

[15]	Wang Y. c-normality of groups and its properties. J Algebra, 1996, 180, 954-965

[16]	Zhang Q., Wang L. The influence of s-semipermutable properties of subgroups on the structure of finite groups. Acta Mathematica Sinica, 2005, 48 1 81-88