Timeline for Conjugacy classes of PGL(3,Z)
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 9, 2013 at 23:19 | history | edited | Alex B. | CC BY-SA 3.0 |
removed the false assertion about the centre.
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| Oct 9, 2013 at 23:17 | comment | added | Alex B. | @Yves Sorry, I was being silly and was thinking of SL. | |
| Oct 9, 2013 at 22:46 | comment | added | SashaKolpakov | @AlexB.: I thought that the centre of $GL(3,\mathbb Z)$ was $\mathbb Z_2$. | |
| Oct 9, 2013 at 17:28 | comment | added | YCor | @Alex: no, the center of $GL(3,\mathbb{Z})$ is not trivial. | |
| Oct 9, 2013 at 16:19 | comment | added | Alex B. | @DerekHolt: indeed, Derek! Otherwise proving that they are non-isomorphic would be even easier of course. It is also worth mentioning that this sort of analysis will solve this question in any given dimension (the list of indecomposables will be the same), although in even dimension one would need to complement it by a similar analysis of modules under the cyclic group of order 6 if one wanted an answer in ${\rm PGL}$, rather than in ${\rm GL}$. | |
| Oct 9, 2013 at 15:38 | comment | added | Derek Holt | It is also worth pointing out that each of the two modules occurs as a submodule of finite index in the other. They are equivalent over ${\mathbb Q}$. | |
| Oct 9, 2013 at 14:43 | history | answered | Alex B. | CC BY-SA 3.0 |