On a Problem of Minimal Non-FC

Abstract

In this paper Problem 17.13 by A.O. Asar in The Kourovka Notebook is studied which is 'Let G be a totally imprimitive p - group of finitary permutations on an infinite set. Suppose that the support of any cycle in the cyclic decomposition of every element of G is a block for G. Does G necessarily contain a minimal non - FC - subgroup?' and an example of a group G satisfying these conditions but not having a minimal non - FC - subgroup is given. © 2016 Academic Publications, Ltd.