Weakly <italic>s</italic>-semipermutable subgroups of finite groups

doi:10.1007/s11464-010-0081-x

Front Math Chin

2011, Vol. 6

Issue (1) : 161-175 https://doi.org/10.1007/s11464-010-0081-x

RESEARCH ARTICLE

Weakly s-semipermutable subgroups of finite groups

Yong XU, Xianhua LI(

)

School of Mathematical Science, Soochow University, Suzhou 215006, China

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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 p² 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

Corresponding Author(s): LI Xianhua,Email:xhli@suda.edu.cn

Issue Date: 01 February 2011

Cite this article:

Yong XU,Xianhua LI. Weakly s-semipermutable subgroups of finite groups[J]. Front Math Chin, 2011, 6(1): 161-175.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-010-0081-x
https://academic.hep.com.cn/fmc/EN/Y2011/V6/I1/161

1	Ballester-Bolinches A. ?-normalizers and local definitions of saturated formations of finite groups. Israel J Math, 1989, 67: 312-326 doi: 10.1007/BF02764949
2	Ballester-Bolinches A, Pedraza-Aguilera M C. On minimal subgroups of finite groups. Acta Math Hungar, 1996, 73: 335-342 doi: 10.1007/BF00052909
3	Chen Zhongmu. Inner Outer Σ-Group and Minimal Non Σ-Group.Chongqing: Southeast Normal University Press, 1988 (in Chinese)
4	Chen Zhongmu. 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 doi: 10.2307/1994638
6	Doerk K, Hawkes T. Finite Solvable Groups.Berlin: Walter de Gruyter, 1992 Weakly s-semipermutable subgroups of finite groups 175
7	Guo W. The Theory of Classes of Groups.Beijing, New York: Science Press-Kluwer Academic Publishers, 2000
8	Guo X, Shum K P. Cover-avoidance properties and the structure of finite groups. J Pure Appl Algebra, 2003, 181: 297-308 doi: 10.1016/S0022-4049(02)00327-4
9	Huppert B. Endliche Gruppen I.New York: Springer, 1967
10	Huppert B, Blackburn N. Finite Groups III. Berlin-New York: Springer-Verlag, 1982
11	Kegel O H. Sylow-Gruppen and Subnormalteiler endlicher Gruppen. Math Z, 1962, 78: 205-211 doi: 10.1007/BF01195169
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 doi: 10.1007/s10474-005-0225-8
14	Skiba A N. On weakly s-permutable subgroups of finite groups. J Algebra, 2007, 315(1): 192-209 doi: 10.1016/j.jalgebra.2007.04.025
15	Wang Yanming. c-normality of groups and its properties. J Algebra, 1996, 180: 954-965 doi: 10.1006/jabr.1996.0103
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

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