Every infinite group can be generated by P-small subset


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




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


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.


Download data is not yet available.

Author Biographies

Dikran Dikranjan, Università di Udine

Dipartimento diMatematica e Informatica

Igor V. Protasov, Kyiv University

Departament of Cybernetics


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.


How to Cite

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.



Regular Articles