Timeline for Are all free groups linear, i.e., admit a faithful representation to GL(n,K) for some field K ?
Current License: CC BY-SA 3.0
11 events
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| Sep 27, 2017 at 9:35 | comment | added | YCor | (typo in my previous comment: I meant: fully residually linear is the same as residually linear, and the same as residually finite) | |
| Mar 13, 2015 at 10:39 | comment | added | HJRW | @YCor, sorry, yes, I meant `fully residually linear of dimensions $d$'. | |
| Mar 13, 2015 at 7:24 | comment | added | YCor | @HJRW: it it a typo? fully residually linear is the same as linear, and the same as residually finite. You mean in some given dimension? | |
| Mar 13, 2015 at 4:36 | comment | added | HJRW | The fact that 'locally fully residually linear' implies linear was noticed by Tarski. | |
| Mar 21, 2013 at 9:10 | comment | added | YCor | Thanks for the correction, I added "locally" before "fully residually free". | |
| Mar 21, 2013 at 9:08 | history | edited | YCor | CC BY-SA 3.0 |
added 8 characters in body
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| Mar 20, 2013 at 21:35 | comment | added | shane.orourke | One clarification: locally fully residually free groups account for all subgroups of ultrapowers of free groups, however not all subgroups of the latter are fully residually free: in particular ${}^\ast F_2$ itself is not residually free. | |
| Mar 20, 2013 at 21:35 | comment | added | shane.orourke |
This argument shows that locally linear (of bounded degree) implies linear. In fact if I'm not mistaken, one can replace locally' here by fully residually': an easy modification of the argument establishes this.
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| Mar 20, 2013 at 8:35 | vote | accept | Dietrich Burde | ||
| Mar 20, 2013 at 19:30 | |||||
| Mar 19, 2013 at 21:13 | history | edited | YCor | CC BY-SA 3.0 |
1 typo
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| Mar 19, 2013 at 16:07 | history | answered | YCor | CC BY-SA 3.0 |