Timeline for Variation of centraliser in $\operatorname{GL}(n,\mathbb{Z})$

8 events

when toggle format	what		by	license	comment
Dec 13, 2020 at 20:51	history	edited	Geoff Robinson	CC BY-SA 4.0	typos
Dec 13, 2020 at 19:12	history	edited	Geoff Robinson	CC BY-SA 4.0	edited body
Dec 13, 2020 at 18:01	history	edited	Geoff Robinson	CC BY-SA 4.0	Made further remarks
Dec 13, 2020 at 17:20	comment	added	YCor		Sure. Anyway it would be quite off-topic thus interpreted. (If $K$ is a $2\times 2$ matrix defining a symplectic form, the group is all of $\mathrm{SL}_2(\mathbf{Z})$...)
Dec 13, 2020 at 17:08	comment	added	Geoff Robinson		The first question is a matter of interpretation, but the question definitely says, "given $K$ ,is $C^{\prime}(K)$ a finite group?" My (admittedly simple( answer is "not in general", which no-one else had seemed to explicitly say.,
Dec 13, 2020 at 16:38	comment	added	YCor		Actually I understood the first question as whether there's an algorithm with input $K$ and answering yes/no (whence the "given $K$" in the question). It's indeed quote clear to find $K$ with infinite isotropy group (since we obtain all arithmetic orthogonal groups) in this way).
Dec 13, 2020 at 16:30	history	edited	Geoff Robinson	CC BY-SA 4.0	Added explanation.
Dec 13, 2020 at 16:22	history	answered	Geoff Robinson	CC BY-SA 4.0