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A variation on the unique product property

A variation on the unique product property
A variation on the unique product property
We describe a variation on the unique product property of groups, which seems natural from a geometric point of view. It is stronger than the unique product property, and hence implies, for example, that the groups rings have no zero divisors. We describe some of its closure properties under extentions and amalgamated free products. We show that most surface groups satisfy this condition, and give various other examples. We explain how these ideas can give a more geometric interpretation of Promislow's example of a non-u.p. group.
0024-6107
813-826
Bowditch, B.H.
8f3cf0c9-0a10-4b70-8648-33fb2ade7ac9
Bowditch, B.H.
8f3cf0c9-0a10-4b70-8648-33fb2ade7ac9

Bowditch, B.H. (2000) A variation on the unique product property. Journal of the London Mathematical Society, 62 (3), 813-826. (doi:10.1112/S0024610700001307).

Record type: Article

Abstract

We describe a variation on the unique product property of groups, which seems natural from a geometric point of view. It is stronger than the unique product property, and hence implies, for example, that the groups rings have no zero divisors. We describe some of its closure properties under extentions and amalgamated free products. We show that most surface groups satisfy this condition, and give various other examples. We explain how these ideas can give a more geometric interpretation of Promislow's example of a non-u.p. group.

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Published date: 2000

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Local EPrints ID: 29773
URI: https://eprints.soton.ac.uk/id/eprint/29773
ISSN: 0024-6107
PURE UUID: f72489c5-a2d4-4c69-b965-8cbbd02c4caa

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Date deposited: 20 Jul 2006
Last modified: 17 Jul 2017 15:57

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Author: B.H. Bowditch

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