Timeline for Relative property (T) and normal closure
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 23, 2020 at 4:57 | comment | added | YCor | Meant normal subgroup of $\Gamma'$, sorry. | |
| Jan 22, 2020 at 21:58 | comment | added | YCor | Also in my paper Relative Kazhdan Property, Proposition 1.13: I showed that there is a group $\Gamma$ (lattice in some semisimple group) with some infinite subgroup $\Lambda$ such that $(\Gamma,\Lambda)$ has relative Property T, but such that for every subgroup $\Gamma'$ of $\Gamma$ and normal infinite subgroup $\Lambda'$ of $\Gamma$, the pair $(\Gamma',\Lambda')$ does not have relative Property T. | |
| Jan 22, 2020 at 21:53 | comment | added | YCor | Clearly no: for instance when $H$ is finite $H^G$ can be large. For instance in a free product $G=H\ast K$ with $H,K\neq 1$ and $K$ having Property T the answer is always no. It's even false when $H$ is a commensurated subgroup, using slightly more refined counterexamples, such as $\mathbf{Z}[1/2]^2\rtimes (\langle 2\rangle \mathrm{SL}_2(\mathbf{Z}))$. | |
| Jan 22, 2020 at 21:49 | history | edited | YCor |
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| Jan 22, 2020 at 21:40 | review | First posts | |||
| Jan 23, 2020 at 4:53 | |||||
| Jan 22, 2020 at 21:37 | history | asked | Anonymous | CC BY-SA 4.0 |