Geodesic
On the lattice of f-subgroups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 600-613.

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In this paper we introduce the notions of f-subgroups and normal f-subgroups as natural generalizations of subgroups, normal subgroups and group topologies. It will be proved that the set of all f-subgroups on a group is a lattice containing the lattice of all normal f-subgroups as a sublattice. Some open questions are also presented.
Keywords: group topology, f-subgroup, normal f-subgroup. 
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H. Khass; A. R. Ashrafi; B. Bazigaran. On the lattice of f-subgroups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 600-613. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a16/

[1] A. Berarducci, D. Dikranjan, M. Forti, S. Watson, “Cardinal invariants and independence results in the poset of precompact group topologies”, J. Pure Appl. Algebra, 126 (1998), 19–49 | DOI | MR | Zbl

[2] A. Breaz, G. Calugareanu, “Abelian groups whose subgroup lattice is the union of two intervals”, J. Aust. Math. Soc., 78:1 (2005), 27–36 | DOI | MR | Zbl

[3] D. Dikranjan, M. Megrelishvili, “Minimality conditions in topological groups”, Recent progress in general topology. III, Atlantis Press, Paris, 2014, 229–327 | DOI | MR | Zbl

[4] H. Khass, B. Bazigaran, “An introduction to right and left topological group”, 8th international seminar on geometry and topology (Dec. 13–17, 2015)

[5] A. A. Klyachko, A. Y. Olshanskii, D. V. Osin, “On topologizable and non-topologizable groups”, Topology Appl., 160:16 (2013), 2104–2120 | DOI | MR | Zbl

[6] A. A. Klyachko, Are infinite groups "locally topologizable"?, MathOverflow.net, version: 2014-08-23, http://mathoverflow.net/q/179233

[7] M. Lamper, “Complements in the lattice of all topologies of topological groups”, Arch. Math. (Brno), 10:4 (1974), 221–230 | MR

[8] C. E. McPhail, “Hausdorffness in varieties of topological groups”, Bull. Austral. Math. Soc., 57:1 (1998), 147–151 | DOI | MR | Zbl

[9] A. Y. Ol'shanskii, Geometry of Defining Relations in Groups, Translated from the 1989 Russian original by Yu. A. Bakhturin, Mathematics and its Applications (Soviet Series), 70, Kluwer Academic Publishers Group, Dordrecht, 1991 | DOI | MR

[10] P. P. Pálfy, “Groups and Lattices”, Groups St. Andrews 2001 in Oxford, v. II, London Math. Soc. Lecture Note Ser., 305, Cambridge Univ. Press, Cambridge, 2003, 428–454 | MR | Zbl

[11] I. R. Prodanov, L. N. Stojanov, “Every minimal abelian group is precompact”, C. R. Acad. Bulgare Sci., 37:1 (1984), 23–26 | MR | Zbl

[12] M. Suzuki, Structure of a group and the structure of its lattice of subgroups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, 10, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1956 | MR | Zbl

[13] M. Suzuki, Group Theory I, Grundlehren der Mathematischen Wissenschaften, 247, Springer-Verlag, Berlin–New York, 1982 | DOI | MR | Zbl