Timeline for Simplicity of infinite groups
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 23, 2013 at 1:07 | comment | added | Thomas | Actually, I use a^-1b^-1ab, but a^-1=a anyway in this group, so it is ab^-1ab | |
| Aug 22, 2013 at 15:00 | comment | added | Thomas | Woops, didn't see the last part. Sorry. Still, how do I check? | |
| Aug 22, 2013 at 14:54 | comment | added | Thomas | That it is what? Infinite? Simple? Also, how will I be able to check? Some group theory program? By hand? | |
| Aug 22, 2013 at 14:51 | comment | added | Neil Hoffman | I think you may be able to check that the group normally generated by $[a,b]^{10}, ([a,b]^4 b)^n$ for $n\geq 7$ is infinite index in $\langle a, b| a^2,b^3,c^7\rangle$, which is an index 2 subgroup of a hyperbolic triangle group. | |
| Aug 22, 2013 at 14:49 | history | edited | Neil Hoffman | CC BY-SA 3.0 |
Explained the differences in the computation with different definitions for [a,b].
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| Aug 22, 2013 at 14:25 | comment | added | Thomas | I also checked what you said earlier, and you're right, magma should show infinity, but it shows zero because it couldn't figure it out. Is there a way to check whether it is infinite? Also, are there any other groups theory calculators that you recommend? | |
| Aug 22, 2013 at 12:41 | comment | added | Thomas | I checked on magma, and the presentation you used does result in the trivial group, so they are different. | |
| Aug 22, 2013 at 11:44 | history | edited | Neil Hoffman | CC BY-SA 3.0 |
added 24 characters in body
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| Aug 22, 2013 at 11:44 | comment | added | Thomas | [a,b]=ab^-1ab, not abab^-1, I'm not sure, but it may make a difference. | |
| Aug 22, 2013 at 11:22 | history | answered | Neil Hoffman | CC BY-SA 3.0 |