Timeline for Infinite, finitely generated linear group has indices of subgroups divisible by infinitely many primes
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 15, 2021 at 12:32 | answer | added | YCor | timeline score: 3 | |
| Jun 15, 2021 at 12:32 | history | edited | YCor |
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| Jun 14, 2021 at 8:13 | comment | added | YCor | This might be true anyway using congruences subgroups, some Weisfeiler-like phenomenon and some ring theory (every infinite f.g. $F_p$-algebra has residual fields of arbitrary large cardinal). I'll think about it. | |
| Jun 14, 2021 at 8:09 | comment | added | YCor | [This is almost already said in your post] If $K$ has characteristic zero, for all but finitely many $p$, $G$ is virtually residually $p$. Hence for every large enough prime $p$, there exists $m$ such that $G$ has subgroups of index $mp^k$ for infinitely many values of $k$. — If $K$ has characteristic $p$, $G$ might be only virtually residually-$\ell$ for $\ell=p$ so this approach fails. | |
| Jun 14, 2021 at 4:06 | history | asked | spin | CC BY-SA 4.0 |