On cover-avoiding subgroups of Sylow subgroups of finite groups

Yangming Li

Rendiconti del Seminario Matematico della Università di Padova (2010)

  • Volume: 123, page 249-258
  • ISSN: 0041-8994

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Li, Yangming. "On cover-avoiding subgroups of Sylow subgroups of finite groups." Rendiconti del Seminario Matematico della Università di Padova 123 (2010): 249-258. <http://eudml.org/doc/240353>.

@article{Li2010,
author = {Li, Yangming},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {saturated formations; finite groups; cover-avoiding subgroups; CAP-subgroups; generalized Fitting subgroup; chief factors; maximal subgroups; Sylow subgroups},
language = {eng},
pages = {249-258},
publisher = {Seminario Matematico of the University of Padua},
title = {On cover-avoiding subgroups of Sylow subgroups of finite groups},
url = {http://eudml.org/doc/240353},
volume = {123},
year = {2010},
}

TY - JOUR
AU - Li, Yangming
TI - On cover-avoiding subgroups of Sylow subgroups of finite groups
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2010
PB - Seminario Matematico of the University of Padua
VL - 123
SP - 249
EP - 258
LA - eng
KW - saturated formations; finite groups; cover-avoiding subgroups; CAP-subgroups; generalized Fitting subgroup; chief factors; maximal subgroups; Sylow subgroups
UR - http://eudml.org/doc/240353
ER -

References

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  1. [1] M. Asaad, On maximal subgroups of finite group, Comm. Algebra, 26 (11) (1998), pp. 3647--3652. Zbl0915.20008MR1647102
  2. [2] A. Ballester-Bolinches - L. M. Ezquerro - A. N. Skiba, Subgroups of finite group with strong Cover-avoidance property, Bull. Austral. Math. Soc., 79 (2009), pp. 409--506. Zbl1184.20014MR2505354
  3. [3] A. Ballester-Bolinches - L. M. Ezquerro - A. N. Skiba, Local embeddings of some families of subgroups of finite group, Acta Math. Sinica, Eng. Ser., 25 (2009), pp. 869--882. Zbl1190.20014MR2511532
  4. [4] R. Doerk - T. Hawkes, Finite soluble groups. Berlin-New York: Walter De Gruyter, 1992. Zbl0753.20001MR1169099
  5. [5] L. M. Ezquerro, A contribution to the theory of finite supersolvable groups, Rend. Sem. Mat. Univ. Padova, 89 (1993), pp. 161--170. Zbl0809.20009MR1229050
  6. [6] Y. Fan - X. Y. Guo - K. P. Shum, Remarks on two generalizations of normality of subgroups, Chinese Ann. Math., 27A (2) (2006), pp. 169--176 (in Chinese). Zbl1109.20017MR2239430
  7. [7] W. Gaschütz, Praefrattinigruppen, Arch. Math., 13 (1962), pp. 418--426. Zbl0109.01403MR146262
  8. [8] J. D. Gillam, Cover-avoid subgroup in finite solvable groups, J. Algebra, 29 (1974), pp. 324--329. Zbl0293.20017MR346050
  9. [9] D. Gorenstein - R. Lyons - R. Solomon, The Classification of the Simple Finite Groups, Amer. Math. Soc., Providence Rhode Island, 1994. Zbl0816.20016MR1303592
  10. [10] X. Y. Guo - P. F. Guo - K. P. Shum, On semi-cover-avoiding subgroups of finite groups, J. Pure Appl. Algebra, 209 (2007), pp. 151--158. Zbl1117.20013MR2292123
  11. [11] B. Huppert, Endliche Gruppen I, Berlin-New York: Springer-Verlag, 1967. Zbl0412.20002MR224703
  12. [12] B. Huppert - N. Blackburn, Finite Groups III, Berlin-New York: Springer-Verlag, 1982. Zbl0514.20002MR662826
  13. [13] Y. Li - S. Qiao - Y. Wang, On weakly s-permutably embedded subgroups of finite groups, Comm. Algebra, 37 (3) (2009), pp. 1086--1097. Zbl1177.20036MR2503195
  14. [14] Y. Li - G. Wang, A note on maximal CAP subgroups of finite groups, Algebras, Groups and Geometries, 23 (2006), pp. 285--290. Zbl1138.20017MR2303510
  15. [15] B. Li - Z. Zhang, The influence of s-conditionally permutable subgroups on finite groups, Sci. China Ser. A, 52 (2) (2009), pp. 301--310. Zbl1181.20022MR2491730
  16. [16] J. A. Petrillo, The cover-avoidance property in finite groups, PhD thesis, State University of New York at Binghamton, 2003. MR2705048
  17. [17] A. N. Skiba, On weakly s-permutable subgroups of finite groups, J. Algebra, 315 (2007), pp. 192--209. Zbl1130.20019MR2344341
  18. [18] M. J. Tomkinson, Cover-avoidance properties in finite solvable groups, Canad. Math. Bull., 19 (2) (1976), pp. 213--216. Zbl0352.20018MR432754
  19. [19] Y. Wang, C -normality of groups and its properties, J. Algebra, 180 (1996), pp. 954--965. Zbl0847.20010MR1379219
  20. [20] M. Weinstein (editor), Between nilpotent and solvable, Polygonal Publishing House, Passaic (1982). Zbl0488.20001MR655785
  21. [21] Guo Xiuyun - K. P. Shum, Cover-avoidance properties and the structure of finite groups, J. Pure Applied Algebra, 181 (2003), pp. 297--308. Zbl1028.20014MR1975303

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