IJPAM: Volume 108, No. 2 (2016)

ON A PROBLEM OF MINIMAL NON-FC-GROUPS

Yıldız Aydın
Department of Mathematics
Faculty of Art and Science
Ondokuz Mayis University
Samsun, Turkey

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.

Received: February 16, 2016

Revised: February 16, 2016

Published: October 1, 2016

AMS Subject Classification: 20B35, 20F24, 20F05

Key Words and Phrases: minimal non-FC-group, finitary symmetric group
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Bibliography

1
D.J.S. Robinson, A Course in the Theory of Groups, Springer-Verlag, New York (1982).

2
J.D. Dixon, B. Mortimer, Permutation Groups, Springer-Verlag, New York (1996).

3
M.J. Tomkinson, FC-Groups, Pitman Advanced Publishing Program, Boston-London-Melbourne (1984).

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DOI: 10.12732/ijpam.v108i2.16 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 2
Pages: 421 - 423


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