On supplements of subgroups of finite groups

Xianhua Li; A. Ballester-Bolinches

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 3, page 567-574
  • ISSN: 0392-4033

Abstract

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In this paper the concept of s-pair for a subgroup of a finite group is introduced and studied. It provides a uniform way to study the influence of some families of subgroups on the structure of a finite group. A criterion for a finite group to belong to a saturated formation and necessary and sufficient conditions for solubility, supersolvability and nilpotence of a finite group are given.

How to cite

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Li, Xianhua, and Ballester-Bolinches, A.. "On supplements of subgroups of finite groups." Bollettino dell'Unione Matematica Italiana 9-B.3 (2006): 567-574. <http://eudml.org/doc/289633>.

@article{Li2006,
abstract = {In this paper the concept of s-pair for a subgroup of a finite group is introduced and studied. It provides a uniform way to study the influence of some families of subgroups on the structure of a finite group. A criterion for a finite group to belong to a saturated formation and necessary and sufficient conditions for solubility, supersolvability and nilpotence of a finite group are given.},
author = {Li, Xianhua, Ballester-Bolinches, A.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {567-574},
publisher = {Unione Matematica Italiana},
title = {On supplements of subgroups of finite groups},
url = {http://eudml.org/doc/289633},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Li, Xianhua
AU - Ballester-Bolinches, A.
TI - On supplements of subgroups of finite groups
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/10//
PB - Unione Matematica Italiana
VL - 9-B
IS - 3
SP - 567
EP - 574
AB - In this paper the concept of s-pair for a subgroup of a finite group is introduced and studied. It provides a uniform way to study the influence of some families of subgroups on the structure of a finite group. A criterion for a finite group to belong to a saturated formation and necessary and sufficient conditions for solubility, supersolvability and nilpotence of a finite group are given.
LA - eng
UR - http://eudml.org/doc/289633
ER -

References

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  1. BALLESTER-BOLINCHES, A., On the normal index of maximal subgroups in finite groups, J. Pure and Applied Algebra, 147 (1990), 113-118. Zbl0699.20016
  2. BALLESTER-BOLINCHES, A., Saturated formations, theta pairs and completions in finite groups, Siberian Math. J., 37 (2) (1996), 207-212. Zbl0878.20011
  3. BALLESTER-BOLINCHES, A. - GUO, XIUYUN and WANG, YANMING, c-supplemented subgroups of finite groups, Glasgow Math. J., 42 (3) (2000), 383-389. Zbl0968.20009
  4. CONWAY, J. H. - CURTIS, R. T. - NORTON, S. P. - PARKER, R. A., and WILSON, R. A., Atlas of finite groups, Oxford University Press, Eynsham, 1985. Zbl0568.20001
  5. DESKINS, W. E., On maximal subgroups, Proc. Symp. Pure Math., Amer. Math. Soc., 1 (1959), 100-104. Zbl0096.24801
  6. DOERK, K. and HAWKES, T., Finite Soluble Groups, Walter De Gruyter. Berlin/New York, 1992. Zbl0753.20001
  7. GURALNICK, R. M., Subgroups of Prime Power Index in a Simple Group, J. Algebra, 81 (1983), 304-311. Zbl0515.20011
  8. MUKHERJEE, N. P. and BHATTACHARYA, P., On Theta Pairs for A Maximal Subgroup, Proc. Amer. Math. Soc., 109 (3) (1990), 589-596. Zbl0699.20019
  9. WANG, Y., C-Normality of Groups and its properties, J. of Algebra, 180 (1996), 954-965. Zbl0847.20010
  10. YAOQING, ZHAO, On the Deskins completions, theta completions and theta Pairs for maximal subgroups, Comm. Algebra, 26 (10) (1998), 3141-3153. Zbl0911.20017
  11. YAOQING, ZHAO and SHIRONG, LI, On Theta Pairs for Maximal Subgroups, J. Pure and Applied Algebra, 147 (2000), 133-142. Zbl0981.20010

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