Every infinite group can be generated by P-small subset

Authors

  • Dikran Dikranjan Università di Udine
  • Igor V. Protasov Kyiv University

DOI:

https://doi.org/10.4995/agt.2006.1929

Keywords:

Group, Large set, Small set, P-small set

Abstract

For every infinite group G and every set of generators S of G, we construct a system of generators in S which is small in the sense of Prodanov.

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Author Biographies

Dikran Dikranjan, Università di Udine

Dipartimento diMatematica e Informatica

Igor V. Protasov, Kyiv University

Departament of Cybernetics

References

A. Bella and V. Malykhin, Small, large and other subsets of a group, Questions and Answers in General Topology 17 (1967), 183–197.

D. Dikranjan, U. Marconi and R. Moresco, Groups with small set of generators, Applied General Topology 4 (2) (2003), 327–350.

R. Gusso, Large and small sets with respect to homomorphisms and products of groups, Applied General Topology 3 (2) (2002), 133–143.

V.Malykhin and R. Moresco, Small generated groups, Questions and Answers in General Topology 19 (1) (2001), 47–53.

Iv. Prodanov, Some minimal group topologies are precompact, Math.Ann. 227 (1977), 117–125. http://dx.doi.org/10.1007/BF01350188

I. Protasov, Every infinite group can be generated by small subset, in: Third Intern. Algebraic Conf. in Ukraine, Sumy, (2001), 92–94.

I. Protasov and T. Banakh, Ball Structures and Colorings of Graphs and Groups, Matem. Stud. Monogr. Series, Vol 11, Lviv, 2003.

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How to Cite

[1]
D. Dikranjan and I. V. Protasov, “Every infinite group can be generated by P-small subset”, Appl. Gen. Topol., vol. 7, no. 2, pp. 265–268, Oct. 2006.

Issue

Section

Regular Articles