On a problem of minimal non-FC-groups

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Aydin Y.

International Journal of Pure and Applied Mathematics, vol.108, no.2, pp.421-423, 2016 (Scopus)

• Publication Type: Article / Article
• Volume: 108 Issue: 2
• Publication Date: 2016
• Doi Number: 10.12732/ijpam.v108i2.16
• Journal Name: International Journal of Pure and Applied Mathematics
• Journal Indexes: Scopus
• Page Numbers: pp.421-423
• Keywords: Finitary symmetric group, Minimal non-FC-group
• Ondokuz Mayıs University Affiliated: Yes

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.