Groups of homeomorphisms and normal subgroups of the group of permutations
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.
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000650 |
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doaj-b79b00527cc945149d9298f5717972282020-11-24T22:08:35ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114347548010.1155/S0161171291000650Groups of homeomorphisms and normal subgroups of the group of permutationsP. T. Ramachandran0Department of Mathematics, Calicut University P.O., Pin 673 635, IndiaIn 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.http://dx.doi.org/10.1155/S0161171291000650 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
P. T. Ramachandran |
| spellingShingle |
P. T. Ramachandran Groups of homeomorphisms and normal subgroups of the group of permutations International Journal of Mathematics and Mathematical Sciences |
| author_facet |
P. T. Ramachandran |
| author_sort |
P. T. Ramachandran |
| title |
Groups of homeomorphisms and normal subgroups of the group of permutations |
| title_short |
Groups of homeomorphisms and normal subgroups of the group of permutations |
| title_full |
Groups of homeomorphisms and normal subgroups of the group of permutations |
| title_fullStr |
Groups of homeomorphisms and normal subgroups of the group of permutations |
| title_full_unstemmed |
Groups of homeomorphisms and normal subgroups of the group of permutations |
| title_sort |
groups of homeomorphisms and normal subgroups of the group of permutations |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1991-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/S0161171291000650 |
| work_keys_str_mv |
AT ptramachandran groupsofhomeomorphismsandnormalsubgroupsofthegroupofpermutations |
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