The structure of finite groups and ɵ-pairs of general subgroups

• Autorzy: Yong Xu , Hailong Hou , Xinjian Zhang
• Języki publikacji: EN

Abstrakty

EN

Using the concept of ɵ-pairs of proper subgroups of a finite group, we obtain some critical conditions of the supersolvability and nilpotency of finite groups.

Słowa kluczowe

EN

Finite group; supersolvable group; Nilpotent group; ɵ-pair

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2015-01-13

zaakceptowano

2015-08-19

online

2015-09-25

Twórcy

autor

Yong Xu

• School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, Henan 471023, China

autor

Hailong Hou

• School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, Henan 471023, China

autor

Xinjian Zhang

• School of Mathematics, Huaiyin Normal University, Huaian, Jiangsu, 223300, China

Bibliografia

• [1] Ballester-Bolinches, A., On saturated formations, theta-pairs and completions in finite groups, Sib. Math. J., 1996, 37(2), 207-212
• [2] Ballester-Bolinches, A., Zhao, Y., On maximal subgroups of finite groups and theta pairs, Comm. Algebra, 1996, 24(13), 4199- 4209
• [3] Guo, X., On theta pairs for maximal subgroup, Comm. Algebra, 1994, 22(4), 4653-4659 [Crossref]
• [4] Huppert, B., Endliche Gruppen I, Springer, New York, Berlin, 1967
• [5] Li, X., Li, S., Theta pair and the structure of finite groups, Sib. Math. J., 2004, 45(3), 557-561
• [6] Li, X., Nan, A., The structure of finite group and the ɵ-pairs of subgroups, Contributions to general algebra 19, Proceedings of the Olomouc Conference 2010, (AAA79+CYA25), Verlag Johannes Heyn, Klagenfurt 2010
• [7] Mukherjee, N., Bhattacharya, P., On theta pairs for a maximal subgroup, Proc. Amer. Math. Soc., 109(3), 1990, 589-596
• [8] Skiba, A., A note on c-normal subgroups of finite groups, Algebra Discrete Math., 2005, 3, 85-95
• [9] Skiba, A., On weakly s-permutable subgroups of finite groups, J. Algebra, 2007, 315(1), 192-209
• [10] Wang, Y., c-normality of groups and its properties, J. Algebra, 1996, 180, 954-965
• [11] Wang, Y., Finite groups with some subgroup of Sylow subgroups c-supplemented, J. Algebra, 2000, 224, 467-478
• [12] Xu, Y., Zhao, T., Li, X., On CISE-normal subgroups of finite groups, Turish J. Math., 2012, 36, 231-243

Identyfikatory

DOI

10.1515/math-2015-0057