Timeline for The Higman group
Current License: CC BY-SA 3.0
24 events
| when toggle format | what | by | license | comment | |
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| Feb 4, 2012 at 16:11 | comment | added | user6976 | See update 4 of my answer below. | |
| Feb 3, 2012 at 9:31 | vote | accept | Kate Juschenko | ||
| Feb 3, 2012 at 9:31 | vote | accept | Kate Juschenko | ||
| Feb 3, 2012 at 9:31 | |||||
| Feb 3, 2012 at 9:30 | vote | accept | Kate Juschenko | ||
| Feb 3, 2012 at 9:31 | |||||
| Feb 3, 2012 at 3:04 | answer | added | user6976 | timeline score: 23 | |
| Feb 3, 2012 at 2:15 | answer | added | Jeff Strom | timeline score: 4 | |
| Feb 2, 2012 at 23:59 | comment | added | Kate Juschenko | @ Mustafa: I think it is the first known fin gen simple group. but I don't know if it fin pres, at least Higman posts this as a question in his paper (and actually the existence of such groups). I would be happy to see later results on this group. | |
| Feb 2, 2012 at 23:51 | comment | added | Junkie | en.wikipedia.org/wiki/Higman_group See the 1974 reference there if you want finitely presented infinite simple groups. | |
| Feb 2, 2012 at 23:49 | comment | added | Mustafa Gokhan Benli | @Kate: I was trying to say that it must be known that the quotient is not finitely presented. I think there are earlier examples of f.p. infinite simple groups. | |
| Feb 2, 2012 at 23:41 | comment | added | Kate Juschenko | @ Mustafa: oh yes, examples would be Burger-Mozes groups | |
| Feb 2, 2012 at 23:40 | comment | added | Steve D | The infinite simple group is not finitely presented, but I don't have a reference at hand. I will look a little bit later tonight. | |
| Feb 2, 2012 at 23:37 | comment | added | Mustafa Gokhan Benli | @Kate,Hi!. As far as I remember Higman asked of examples of finitely presented infinite simple groups. So I always though that this must be known. | |
| Feb 2, 2012 at 23:37 | comment | added | Kate Juschenko | @Mustafa: hi there, I don't think it is known, if it is finitely presented. it is fin gen, of course. | |
| Feb 2, 2012 at 23:33 | history | edited | Kate Juschenko | CC BY-SA 3.0 |
added 1 characters in body
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| Feb 2, 2012 at 23:32 | comment | added | Mustafa Gokhan Benli | I would also like to know where it was proven that the quotient of this group by its maximal normal subgroup is not finitely presented. | |
| Feb 2, 2012 at 23:01 | comment | added | Autumn Kent | @Kate: Oh yes, I agree that it is not clear that the group is simple. Higman does not claim that it is, but merely that once you mod out by the maximal normal subgroup, you get an infinite simple group. I would love to know the answer to your question. +1. | |
| Feb 2, 2012 at 22:53 | comment | added | Kate Juschenko | @Richard: it is still not clear (to me) if it is simple... | |
| Feb 2, 2012 at 22:52 | comment | added | Kate Juschenko | @Richard: thanks for correcting the post. | |
| Feb 2, 2012 at 21:55 | history | edited | Autumn Kent | CC BY-SA 3.0 |
Wrote group as presentation.
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| Feb 2, 2012 at 21:49 | comment | added | Autumn Kent | @Igor: Higman constructs this group in A finitely generated infinite simple group. J. London Math. Soc. 26, (1951). 61--64. | |
| Feb 2, 2012 at 20:01 | comment | added | Ralph | I would had expected the last equation to be $a_3a_0a_3^{-1}=a_0^2$. | |
| Feb 2, 2012 at 19:46 | comment | added | Igor Rivin | Do you have a reference for where this is constructed? | |
| Feb 2, 2012 at 17:58 | history | edited | Colin Reid |
edited tags
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| Feb 2, 2012 at 16:51 | history | asked | Kate Juschenko | CC BY-SA 3.0 |