On some generalization of pronormal subgroups in locally finite group

A.A. Pypka (Oles Honchar Dnipropetrovsk National University)
N.A. Turbay (Oles Honchar Dnipropetrovsk National University)

Abstract


We proved that if every subgroup of locally finite group is monopronormal, then this group is a $$$\overline{T}$$$-group.

Keywords


locally finite group; monopronormal subgroup; contranormal subgroup; Dedekind group; supersoluble group; locally nilpotent residual; $$$\overline{T}$$$-group

Full Text:

PDF

References


Robinson D.J.S. "Groups in which normality is a transitive relation", Proc. Cambridge Philos. Soc., 1964; 60: pp. 21-38. doi:10.1017/S0305004100037403

Subbotin I.Ya., Kuzenny N.F. "Locally soluble groups in which all infinite subgroups are pronormal", Izvestiya VUZ, Math., 1988; 32: pp. 126-131. (in Russian)

Ballester-Bolinches A., Esteban-Romero R. "Sylow permutable subnormal subgroups of finite groups", Journal of Algebra, 2002; 251: pp. 727-738. doi:10.1006/jabr.2001.9138

Baer R. "Durch Formationen bestimmte Zerlegungen von Normalteilern endlicher Gruppen", Journal of Algebra, 1972; 20: pp. 38-56. (in German) doi:10.1016/0021-8693(72)90082-8

Ol’shanskii A. Yu. "Geometry of defining relations in groups", Mathematics and its Applications, 1991; 505 p. doi:10.1007/978-94-011-3618-1




DOI: https://doi.org/10.15421/241513

  

Refbacks

  • There are currently no refbacks.


Copyright (c) 2015 A.A. Pypka, N.A. Turbay

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Registered in

More►


ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
DNU