Timeline for Is It possible to determine whether the given finitely presented group is residually finite with MAGMA or GAP?
Current License: CC BY-SA 4.0
5 events
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| Jul 22, 2022 at 13:07 | comment | added | Max Horn | @ALanKay perhaps you'd be inclined to post your presentation, possible as a separate question: while I don't want to get your hopes up (despite my complaint, Giles is of course fundamentally correct!) but who knows, perhaps it's one of those special cases, or someone has another purely theoretical idea how to deal with it... | |
| Jul 22, 2022 at 13:04 | comment | added | Max Horn | I feel this answer is a bit misleading without qualifying the statement, as Geordie pointed out: of course there is no algorithm that can do this in general, but for specific examples it may still be possible. Also if there is additional information about the group due to how it was constructed, that can change the picture. | |
| Jul 22, 2022 at 10:16 | comment | added | HJRW | There are very few known ways of certifying residual finiteness. Perhaps the most obvious way is to find a faithful representation, but this is very difficult to do in general. (I don't know if GAP or Magma have databases of linear groups to get you started...) One modern approach is to look for a special cubulation, but I don't think there has been much work on doing this effectively. | |
| Jul 22, 2022 at 8:12 | comment | added | Geordie Williamson | On the other hand, magma is rather good at doing some things in special cases which are undecidable in general. (E.g. deciding what a group is from a presentation ...) I'm not aware of any approaches to the OP's problem though... | |
| Jul 22, 2022 at 5:05 | history | answered | Giles Gardam | CC BY-SA 4.0 |