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On uniqueness of JSJ decompositions of finitely generated groups
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UNSPECIFIED (2003) On uniqueness of JSJ decompositions of finitely generated groups. COMMENTARII MATHEMATICI HELVETICI, 78 (4). pp. 740-751. doi:10.1007/s00014-003-0780-y ISSN 0010-2571.
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Official URL: http://dx.doi.org/10.1007/s00014-003-0780-y
Abstract
We give an example of two JSJ decompositions of a group that are not related by conjugation, conjugation of edge-inclusions, and slide moves. This answers the question of Rips and Sela stated in [RS].
On the other hand we observe that any two JSJ decompositions of a group are related by an elementary deformation, and that strongly slide-free JSJ decompositions are genuinely unique. These results hold for the decompositions of Rips and Sela, Dunwoody and Sageev, and Fujiwara and Papasoglu, and also for accessible decompositions.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | COMMENTARII MATHEMATICI HELVETICI | ||||
Publisher: | BIRKHAUSER VERLAG AG | ||||
ISSN: | 0010-2571 | ||||
Official Date: | 2003 | ||||
Dates: |
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Volume: | 78 | ||||
Number: | 4 | ||||
Number of Pages: | 12 | ||||
Page Range: | pp. 740-751 | ||||
DOI: | 10.1007/s00014-003-0780-y | ||||
Publication Status: | Published |
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