IJPAM: Volume 106, No. 3 (2016)

ON $T$-REPRESENTABILITY OF
THE CYCLIC SUBGROUPS OF THE SYMMETRIC GROUP-I

P. Sini$^1$, P.T. Ramachandran$^2$
$^{1,2}$Department of Mathematics
University of Calicut
Malappuram Dt., Pin: 673635, Kerala, INDIA


Abstract. In this paper we investigate the group of homeomorphisms of topological spaces. A subgroup $K$ of the group $S(X)$ of all permutations of a set $X$ is called $t$-representable on $X$ if there exists a topology $T$ on $X$ such that the group of homeomorphisms of $(X,\ T)\,=\,K$. We determine the $t$-representability of groups generated by a permutation which is a product of disjoint cycles having equal lengths.

Received: October 28, 2015

AMS Subject Classification: 54H15, 20B35

Key Words and Phrases: cyclic groups, group of homeomorphisms, permutation groups, t-representable

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DOI: 10.12732/ijpam.v106i3.11 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: 106
Issue: 3
Pages: 851 - 857


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