On locally finite groups whose cyclic subgroups are monopronormal

A.A. Pypka

doi:10.15421/241711

On locally finite groups whose cyclic subgroups are monopronormal

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

Abstract

The description of locally finite groups whose cyclic subgroups are monopronormal was obtained.

Keywords

monopronormal subgroup; locally finite group; locally nilpotent residual

Full Text:

PDF

References

Rose J.S. "Nilpotent subgroups of finite soluble groups", Math. Z., 1968; 106(2): pp. 97-112. doi:10.1007/BF01110717

Ba M.S., Borevich Z.I. "On arrangement of intermediate subgroups", Rings and Linear Groups, 1988; pp. 14-41.

Dedekind R. "Ueber Gruppen, deren sämmtliche Theiler Normaltheiler sind", Math. Ann., 1897; 48(4): pp. 548-561. (in German) doi:10.1007/BF01447922

Baer R. "Situation der Untergruppen, und Struktur der Gruppe", S.-B. Heidelberg Acad. Math.-Nat. Klasse, 1933; 2: pp. 12-17. (in German)

Pypka A.A. Turbay N.A. "On some generalization of pronormal subgroups in locally finite group", Res. Math., 2015; 23: pp. 107-110. doi:10.15421/241513

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

Rose J.S. A course on group theory, Cambridge: Cambridge Univ. Press, 1978; 318 p.

Feit W., Thompson J.G. "Solvability of groups of odd order", Pacific J. Math, 1963; 13(3): pp. 775-787. doi:10.2140/pjm.1963.13.775

Kurosh A.G. The theory of groups, Nauka, Moscow, 1967; 648 p. (in Russian)

McLain D.H. "Finiteness conditions in locally soluble groups", J. London Math. Soc., 1959; 34(1): pp. 101-107. doi:10.1112/jlms/s1-34.1.101

Schmidt R. Subgroups Lattices of Groups, Walter de Gruyter, Berlin, 1994.

Ballester-Bolinches A., Kurdachenko L.A., Otal J., Pedraza T. "Infinite groups with many permutable subgroups", Rev. Mat. Iberoam., 2008; 24(3): pp. 745-764.

Dixon M.R. Sylow theory, formations and Fitting classes in locally finite groups, Singapore: World Scientific, 1994; 304 p.

Chernikov S.N. "On complementability of the Sylow $$$\pi$$$-subgroups in some classes of infinite groups", Matem. sbornik, 1955; 37: pp. 557-566. (in Russian)