On the structure of groups whose non-abelian subgroups are subnormal

Leonid Kurdachenko; Sevgi Atlıhan; Nikolaj Semko

Open Mathematics (2014)

  • Volume: 12, Issue: 12, page 1762-1771
  • ISSN: 2391-5455

Abstract

top
The main aim of this article is to examine infinite groups whose non-abelian subgroups are subnormal. In this sense we obtain here description of such locally finite groups and, as a consequence we show several results related to such groups.

How to cite

top

Leonid Kurdachenko, Sevgi Atlıhan, and Nikolaj Semko. "On the structure of groups whose non-abelian subgroups are subnormal." Open Mathematics 12.12 (2014): 1762-1771. <http://eudml.org/doc/269626>.

@article{LeonidKurdachenko2014,
abstract = {The main aim of this article is to examine infinite groups whose non-abelian subgroups are subnormal. In this sense we obtain here description of such locally finite groups and, as a consequence we show several results related to such groups.},
author = {Leonid Kurdachenko, Sevgi Atlıhan, Nikolaj Semko},
journal = {Open Mathematics},
keywords = {Non-abelian subgroup; Subnormal subgroup; Locally finite group; The Sylow p-subgroup; subnormal subgroups; non-Abelian subgroups; locally finite groups; Sylow subgroups},
language = {eng},
number = {12},
pages = {1762-1771},
title = {On the structure of groups whose non-abelian subgroups are subnormal},
url = {http://eudml.org/doc/269626},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Leonid Kurdachenko
AU - Sevgi Atlıhan
AU - Nikolaj Semko
TI - On the structure of groups whose non-abelian subgroups are subnormal
JO - Open Mathematics
PY - 2014
VL - 12
IS - 12
SP - 1762
EP - 1771
AB - The main aim of this article is to examine infinite groups whose non-abelian subgroups are subnormal. In this sense we obtain here description of such locally finite groups and, as a consequence we show several results related to such groups.
LA - eng
KW - Non-abelian subgroup; Subnormal subgroup; Locally finite group; The Sylow p-subgroup; subnormal subgroups; non-Abelian subgroups; locally finite groups; Sylow subgroups
UR - http://eudml.org/doc/269626
ER -

References

top
  1. [1] Ballester-Bolinches, Kurdachenko L.A., Otal J., Pedraza T., Infinite groups with many permutable subgroups, Rev. Mat. Iberoam., 2008, 24(3), 745–764 http://dx.doi.org/10.4171/RMI/555 Zbl1175.20036
  2. [2] Berkovich Y., Groups of Prime Power Order, vol. 1, de Gruyter Exp. Math., 46, Berlin, 2008 
  3. [3] Dixon M.R., Sylow Theory, Formations and Fitting classes in Locally Finite Groups, World Sci. Publ. Co., Singapore, 1994 http://dx.doi.org/10.1142/2386 
  4. [4] Dixon M.R., Subbotin I.Ya., Groups with finiteness conditions on some subgroup systems: a contemporary stage, Algebra Discrete Math., 2009, 4, 29–54 Zbl1199.20051
  5. [5] Hall P., Some sufficient conditions for a group to be nilpotent, Illinois J. Math., 1958, 2, 787–801 Zbl0084.25602
  6. [6] Knyagina V.N., Monakhov V.S., On finite groups with some subnormal Schmidt subgroups, Sib. Math. J., 2004, 45(6), 1316–1322 http://dx.doi.org/10.1023/B:SIMJ.0000048922.59466.20 Zbl1096.20022
  7. [7] Kurdachenko L.A., Otal J., Subbotin I.Ya., Groups with Prescribed Quotient Groups and Associated Module Theory, World Sci. Publ. Co., New Jersey, 2002 Zbl1019.20001
  8. [8] Kurdachenko L.A., Otal J., Subbotin I.Ya., Artian Modules over Group Rings, Front. Math., Birkhäuser, Basel, 2007 Zbl1110.16001
  9. [9] Kurdachenko L.A., Otal J., On the existence of normal complement to the Sylow subgroups of some infinite groups, Carpathian J. Math., 2013, 29(2), 195–200 Zbl1299.20045
  10. [10] Kuzenny N.F., Semko N.N., The structure of soluble non-nilpotent metahamiltonian groups, Math. Notes, 1983, 34(2), 179–188 
  11. [11] Kuzenny N.F., Semko N.N., The structure of soluble metahamiltonian groups, Dokl. Akad. Nauk Ukrain. SSR Ser. A, 1985, 2, 6–8 
  12. [12] Kuzenny N.F., Semko, N.N., On the structure of non-periodic metahamiltonian groups, Russian Math. (Iz. VUZ), 1986, 11, 32–40 
  13. [13] Kuzenny N.F., Semko N.N., The structure of periodic metabelian metahamiltonian groups with a non-elementary commutator subgroup, Ukrainian Math. J., 1987, 39(2), 180–185 
  14. [14] Kuzenny N.F., Semko N.N., The structure of periodic metabelian metahamiltonian groups with an elementary commutator subgroup of rank two, Ukrainian Math. J., 1988, 40(6), 627–633 http://dx.doi.org/10.1007/BF01057181 
  15. [15] Kuzenny N.F., Semko N.N., The structure of periodic non-abelian metahamiltonian groups with an elementary commutator subgroup of rank three, Ukrainian Math. J., 1989, 41(2), 153–158 http://dx.doi.org/10.1007/BF01060379 Zbl0713.20032
  16. [16] Kuzenny N.F., Semko, N.N., Metahamiltonian groups with elementary commutator subgroup of rank two, Ukrainian Math. J., 1990, 42(2), 149–154 http://dx.doi.org/10.1007/BF01071007 
  17. [17] Lennox J.C., Stonehewer S.E., Subnormal Subgroups of Groups, Oxford Math. Monogr., Oxford University Press, New York, 1987 Zbl0606.20001
  18. [18] Mahnev A.A., Finite metahamiltonian groups, Ural. Gos. Univ. Mat. Zap., 1976, 10(1), 60–75 Zbl0414.20016
  19. [19] Möhres W., Auflösbarkcit von Gruppen deren Untergruppen alle subnormal sind., Arch. Math., 1990, 54(3), 232–235 http://dx.doi.org/10.1007/BF01188516 Zbl0663.20027
  20. [20] Nagrebetskij V.T., Finite groups every non-nilpotent subgroup of which is normal, Ural. Gos. Univ. Mat. Zap., 1966, 6(3), 45–49 
  21. [21] Nagrebetskij V.T., Finite nilpotent groups every non-abelian subgroup of which is normal, Ural. Gos. Univ. Mat. Zap., 1967, 6(1), 80–88 
  22. [22] Robinson D.J.S., Finiteness Conditions and Generalized Soluble Groups, vol. 2, Ergeb. Math. Grenzgeb., 63, Springer, Berlin-Heidelberg-New York, 1972 http://dx.doi.org/10.1007/978-3-662-07241-7 
  23. [23] Romalis G.M., Sesekin N.F., Metahamiltonian groups I, Ural. Gos. Univ. Mat. Zap., 1966, 5(3), 101–106 
  24. [24] Romalis G.M., Sesekin N.F., Metahamiltonian groups II, Ural. Gos. Univ. Mat. Zap., 1968, 6(3), 50–52 Zbl0351.20021
  25. [25] Romalis G.M., Sesekin N.F., The metahamiltonian groups III, Ural. Gos. Univ. Mat. Zap., 1970, 7(3), 195–199 Zbl0324.20036
  26. [26] Schur I., Über die Darstellungen der endlichen Gruppen durch gebrochene lineare substitutione, J. Reine Angew. Math., 1904, 127, 20–50 Zbl35.0155.01
  27. [27] Smith H., Torsion free groups with all non-nilpotent subgroups subnormal, In: Topics in infinite groups, Quad. Mat., 8, Seconda Università degli Studi di Napoli, Caserta, 2001, 297–308 Zbl1017.20017
  28. [28] Smith H., Groups with all non-nilpotent subgroup subnormal, In: Topics in infinite groups, Quad. Mat., 8, Seconda Università degli Studi di Napoli, Caserta, 2001, 309–326 Zbl1017.20018
  29. [29] Stonehewer S.E., Formations and a class of locally soluble groups, Proc. Cambridge Phil. Soc., 1966, 62, 613–635 http://dx.doi.org/10.1017/S0305004100040275 Zbl0145.02503
  30. [30] Vedernikov V.A., Finite groups with subnormal Schmidt subgroups, Sib. Algebra Logika, 2007, 46(6), 669–687 Zbl1155.20304

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.