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

Yong Xu; Hailong Hou; Xinjian Zhang

Open Mathematics (2015)

  • Volume: 13, Issue: 1
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Yong Xu, Hailong Hou, and Xinjian Zhang. "The structure of finite groups and ɵ-pairs of general subgroups." Open Mathematics 13.1 (2015): null. <http://eudml.org/doc/275900>.

@article{YongXu2015,
abstract = {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.},
author = {Yong Xu, Hailong Hou, Xinjian Zhang},
journal = {Open Mathematics},
keywords = {Finite group; supersolvable group; Nilpotent group; ɵ-pair},
language = {eng},
number = {1},
pages = {null},
title = {The structure of finite groups and ɵ-pairs of general subgroups},
url = {http://eudml.org/doc/275900},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Yong Xu
AU - Hailong Hou
AU - Xinjian Zhang
TI - The structure of finite groups and ɵ-pairs of general subgroups
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - null
AB - 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.
LA - eng
KW - Finite group; supersolvable group; Nilpotent group; ɵ-pair
UR - http://eudml.org/doc/275900
ER -

References

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  6. [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. [7] Mukherjee, N., Bhattacharya, P., On theta pairs for a maximal subgroup, Proc. Amer. Math. Soc., 109(3), 1990, 589-596 Zbl0699.20019
  8. [8] Skiba, A., A note on c-normal subgroups of finite groups, Algebra Discrete Math., 2005, 3, 85-95 Zbl1092.20018
  9. [9] Skiba, A., On weakly s-permutable subgroups of finite groups, J. Algebra, 2007, 315(1), 192-209 Zbl1130.20019
  10. [10] Wang, Y., c-normality of groups and its properties, J. Algebra, 1996, 180, 954-965 Zbl0847.20010
  11. [11] Wang, Y., Finite groups with some subgroup of Sylow subgroups c-supplemented, J. Algebra, 2000, 224, 467-478 Zbl0953.20010
  12. [12] Xu, Y., Zhao, T., Li, X., On CISE-normal subgroups of finite groups, Turish J. Math., 2012, 36, 231-243 Zbl1262.20020

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