On Hall subgroups of a finite group

Wenbin Guo; Alexander Skiba

Open Mathematics (2013)

  • Volume: 11, Issue: 7, page 1177-1187
  • ISSN: 2391-5455

Abstract

top
New criteria of existence and conjugacy of Hall subgroups of finite groups are given.

How to cite

top

Wenbin Guo, and Alexander Skiba. "On Hall subgroups of a finite group." Open Mathematics 11.7 (2013): 1177-1187. <http://eudml.org/doc/269702>.

@article{WenbinGuo2013,
abstract = {New criteria of existence and conjugacy of Hall subgroups of finite groups are given.},
author = {Wenbin Guo, Alexander Skiba},
journal = {Open Mathematics},
keywords = {Finite group; Hall subgroup; Permutable subgroups; Eµ-group; Cµ-group; Dµ-group; finite groups; Hall subgroups; permutable subgroups; -groups; -groups; -groups; Sylow subgroups; -separable groups},
language = {eng},
number = {7},
pages = {1177-1187},
title = {On Hall subgroups of a finite group},
url = {http://eudml.org/doc/269702},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Wenbin Guo
AU - Alexander Skiba
TI - On Hall subgroups of a finite group
JO - Open Mathematics
PY - 2013
VL - 11
IS - 7
SP - 1177
EP - 1187
AB - New criteria of existence and conjugacy of Hall subgroups of finite groups are given.
LA - eng
KW - Finite group; Hall subgroup; Permutable subgroups; Eµ-group; Cµ-group; Dµ-group; finite groups; Hall subgroups; permutable subgroups; -groups; -groups; -groups; Sylow subgroups; -separable groups
UR - http://eudml.org/doc/269702
ER -

References

top
  1. [1] Ballester-Bolinches A., Esteban-Romero R., Asaad M., Products of Finite Groups, de Gruyter Exp. Math., 53, Walter de Gruyter, Berlin, 2010 http://dx.doi.org/10.1515/9783110220612[Crossref] Zbl1206.20019
  2. [2] Čunihin S.A., On π-separate groups, Doklady Akad. Nauk SSSR (N.S.), 1948, 59, 443–445 (in Russian) 
  3. [3] Čunihin S.A., On weakening the conditions in theorems of Sylow type, Doklady Akad. Nauk SSSR (N.S.), 1952, 83, 663–665 (in Russian) [WoS] 
  4. [4] Čunihin S.A., On existence and conjugateness of subgroups of a finite group, Mat. Sb. (N.S.), 1953, 33(75), 111–132 (in Russian) 
  5. [5] Doerk K., Hawkes T., Finite Soluble Groups, de Gruyter Exp. Math., 4, Walter de Gruyter, Berlin, 1992 http://dx.doi.org/10.1515/9783110870138 Zbl0753.20001
  6. [6] Foguel N., On seminormal subgroups, J. Algebra, 1994, 165(3), 633–635 http://dx.doi.org/10.1006/jabr.1994.1135[Crossref] 
  7. [7] Guo W., Shum K.P., Skiba A.N., X-semipermutable subgroups of finite groups, J. Algebra, 2007, 315(1), 31–41 http://dx.doi.org/10.1016/j.jalgebra.2007.06.002[Crossref] Zbl1130.20017
  8. [8] Guo W.B., Skiba A.N., Criteria of existence of Hall subgroups in non-soluble finite groups, Acta Math. Sin. (Engl. Ser.), 2010, 26(2), 295–304 http://dx.doi.org/10.1007/s10114-010-8034-6[Crossref][WoS] Zbl1213.20018
  9. [9] Guo W., Skiba A.N., New criterions of existence and conjugacy of Hall subgroups of finite groups, Proc. Amer. Math. Soc., 2011, 139(7), 2327–2336 http://dx.doi.org/10.1090/S0002-9939-2010-10675-5[Crossref] Zbl1236.20019
  10. [10] Hall P., A characteristic property of soluble groups, J. London Math. Soc., 1937, s1–12(3), 198–200 http://dx.doi.org/10.1112/jlms/s1-12.2.198[Crossref] 
  11. [11] Hall P., Theorems like Sylow’s, Proc. London Math. Soc., 1956, 6, 286–304 http://dx.doi.org/10.1112/plms/s3-6.2.286[Crossref] Zbl0075.23907
  12. [12] Kegel O.H., Produkte nilpotenter Gruppen, Arch. Math. (Basel), 1961, 12, 90–93 http://dx.doi.org/10.1007/BF01650529[Crossref] Zbl0099.01401
  13. [13] Kegel O.H, Sylow-Gruppen and Subnormalteiler endlicher Gruppen, Math. Z., 1962, 78, 205–221 http://dx.doi.org/10.1007/BF01195169[Crossref] 
  14. [14] Knyagina V.N., Monakhov V.S., On the π′-properties of a finite group possessing a Hall π-subgroup, Sib. Math. J., 2011, 52(2), 234–243 http://dx.doi.org/10.1134/S0037446611020066[Crossref] Zbl1256.20013
  15. [15] Revin D.O., Vdovin E.P., Hall subgroups of finite groups, In: Ischia Group Theory 2004, Naples, March 31–April 3, 2004 Contemp. Math., 402, American Mathematical Society/Bar-Ilan University, Providence/Ramat Gan, 2006, 229–265 
  16. [16] Rusakov S.A., Analogues of Sylow’s theorem on the existence and imbedding of subgroups, Sibirsk. Mat. Zh., 1963, 4(2), 325–342 (in Russian) Zbl0209.33106
  17. [17] Shemetkov L.A., On Sylow properties of finite groups, Dokl. Akad. Nauk BSSR, 1972, 16(10), 881–883 (in Russian) 
  18. [18] Shemetkov L.A., Formations of Finite Groups, Nauka, Moscow, 1978 (in Russian) Zbl0496.20014
  19. [19] Vdovin E.P., Revin D.O., A conjugacy criterion for Hall subgroups in finite groups, Sib. Math. J., 2010, 51(3), 402–409 http://dx.doi.org/10.1007/s11202-010-0041-4[Crossref] Zbl1205.20021
  20. [20] Wielandt H., Zum Satz von Sylow. II, Math. Z., 1959, 71, 461–462 http://dx.doi.org/10.1007/BF01181418[Crossref] Zbl0166.28802
  21. [21] Wielandt H., Subnormal Subgroups and Permutation Groups, Ohio State University, Columbus, 1971 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.