International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 475-480

Groups of homeomorphisms and normal subgroups of the group of permutations

P. T. Ramachandran

Department of Mathematics, Calicut University P.O., Pin 673 635, India

Received 13 February 1989

Copyright © 1991 P. T. Ramachandran. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, it is proved that no nontrivial proper normal subgroup of the group of permutations of a set X can be the group of homeomorphisms of (X,T) for any topology T on X.