Abelian subgroup separability of some one-relator groups
We prove that any group in the class of one-relator groups given by the presentation 〈a,b;[am,bn]=1〉, where m and n are integers greater than 1, is cyclic subgroup separable (or πc). We establish some suitable properties of these groups which enable us to prove that every finitely generated abelian...
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| Language: | English |
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Hindawi Limited
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.2287 |
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doaj-116671136a624d1bb49648026de0a0842020-11-24T21:41:36ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005142287229810.1155/IJMMS.2005.2287Abelian subgroup separability of some one-relator groupsD. Tieudjo0Department of Mathematics and Computer Science, University of Ngaoundere, P.O. Box 454, Ngaoundere, CameroonWe prove that any group in the class of one-relator groups given by the presentation 〈a,b;[am,bn]=1〉, where m and n are integers greater than 1, is cyclic subgroup separable (or πc). We establish some suitable properties of these groups which enable us to prove that every finitely generated abelian subgroup of any of such groups is finitely separable.http://dx.doi.org/10.1155/IJMMS.2005.2287 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
D. Tieudjo |
| spellingShingle |
D. Tieudjo Abelian subgroup separability of some one-relator groups International Journal of Mathematics and Mathematical Sciences |
| author_facet |
D. Tieudjo |
| author_sort |
D. Tieudjo |
| title |
Abelian subgroup separability of some one-relator groups |
| title_short |
Abelian subgroup separability of some one-relator groups |
| title_full |
Abelian subgroup separability of some one-relator groups |
| title_fullStr |
Abelian subgroup separability of some one-relator groups |
| title_full_unstemmed |
Abelian subgroup separability of some one-relator groups |
| title_sort |
abelian subgroup separability of some one-relator groups |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2005-01-01 |
| description |
We prove that any group in the class of one-relator groups given
by the presentation 〈a,b;[am,bn]=1〉, where m
and n are integers greater than 1, is cyclic subgroup separable
(or πc). We establish some suitable properties of these
groups which enable us to prove that every finitely generated
abelian subgroup of any of such groups is finitely separable. |
| url |
http://dx.doi.org/10.1155/IJMMS.2005.2287 |
| work_keys_str_mv |
AT dtieudjo abeliansubgroupseparabilityofsomeonerelatorgroups |
| _version_ |
1725921119623446528 |