Timeline for Kaplansky's unit conjecture and unique products
Current License: CC BY-SA 3.0
3 events
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| Feb 3, 2015 at 15:35 | comment | added | Jean Raimbault | The Craven--Pappas paper also illustrates the difficulty, since they do a lot of rather involved (though elementary) algebra only to obtain the rather feeble (compared to what we know about zero-divisors) conclusion that a certain kind of unit (with explicit restrictions on the support) cannot exist in this group. Since it is in fact the simplest example of a non u.p. group (it has an index 2 subgroup which does have u.p. this is not encouraging about the general case. | |
| Feb 3, 2015 at 15:29 | comment | added | Jean Raimbault | Yes, one of the difficulties in this question is that there are very few examples of groups without the u.p. property, and apart from the fours group they are somehow artificial (apart from Carter's examples all the known ones are generalizations of the original construction of an hyperbolic group without u.p. by Rips--Segev ; see e.g. arxiv.org/abs/1307.0981 by Steenbock). | |
| Jan 26, 2015 at 0:11 | history | answered | Pace Nielsen | CC BY-SA 3.0 |