Timeline for Infinite, finitely generated linear group has indices of subgroups divisible by infinitely many primes

5 events

when toggle format	what		by	license	comment
Jun 18, 2021 at 1:59	comment	added	spin		I see, thanks, that argument seems better.
Jun 17, 2021 at 19:15	comment	added	YCor		For the first argument: in an arbitrary topological space, if a subset $X$ has closure $Y$ and $Y'$ is clopen in $Y$, then $X\cap Y'$ has closure $Y'$ (so no argument using irreducibility or dimension is needed). So, yes, this allows to reduce to connected Zariski closure.
Jun 17, 2021 at 9:47	comment	added	spin		I should have mentioned that my question was motivated from looking at a proof in MR0387428. There they claim the positive answer follows from the result of Platonov (10.4 in Wehrfritz), but in positive characteristic this does not seem to be clear.
Jun 17, 2021 at 9:42	comment	added	spin		Thank you for the answer. Some details, just to make sure I understand the beginning correctly. Let $S$ be the Zariski closure of $G$. Then $S/S^\circ$ is finite. Thus $G/G \cap S^\circ$ is finite, so $G \cap S^\circ$ is finitely generated. Furthermore, The Zariski closure of $G \cap S^\circ$ has the same dimension as $S^\circ$, so it must be equal to $S^\circ$. So we can assume that $G$ has connected Zariski closure $S$.
Jun 15, 2021 at 12:32	history	answered	YCor	CC BY-SA 4.0