Timeline for Two finite groups with the same identical relations?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 15, 2009 at 22:50 | comment | added | Alon Amit | <bangs head on keyboard> of course. I need to think about what my question really ought to be. | |
| Oct 15, 2009 at 22:45 | comment | added | Reid Barton | Yes, they can. If G is abelian, then the set of identical relations of G only remembers its exponent (gcd of the orders of all elements) by similar reasoning. So we can take Z/4 x Z/4, Z/4 x Z/2 x Z/2 for instance. | |
| Oct 15, 2009 at 21:33 | comment | added | Alon Amit | Of course - thanks. How about if the order of the group is fixed? If G and H are non-isomorphic of the same order, can they still have the same identical relations? Thanks again - if nobody notices the comment I'll post this as a separate question. | |
| Oct 15, 2009 at 21:32 | vote | accept | Alon Amit | ||
| Oct 15, 2009 at 19:24 | comment | added | Eric Wofsey | More generally, this will be true for any group G and any product G^n. | |
| Oct 15, 2009 at 18:43 | history | answered | Reid Barton | CC BY-SA 2.5 |