On locally finite groups whose cyclic subgroups are monopronormal

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


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


monopronormal subgroup; locally finite group; locally nilpotent residual

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

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)

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", Dnipr. Univ. Math. Bull., 2015; 23: pp. 107-110.

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

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. 755-787.

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.

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)


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