Timeline for Groups surjecting onto a free group
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Dec 9, 2011 at 11:35 | history | edited | HJRW | CC BY-SA 3.0 |
Added mention of Makanin's algorithm
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| Nov 9, 2011 at 12:51 | comment | added | Igor Rivin | @Alan: thanks, that's very interesting... | |
| Nov 8, 2011 at 18:12 | comment | added | ADL | Also, Marc Lackenby has given a characterisation of Large groups with respect to "the existence of a normal series where successive quotients are finite abelian groups with sufficiently large rank and order". The paper is "A characterisation of large finitely presented groups", J. Algebra 287 (2005) 458–473. | |
| Nov 8, 2011 at 18:10 | comment | added | ADL | Further to the Baumslag-Pride result, there is a result of Gromov and Stohr which says that if G=⟨X;r⟩ has only one more generator than relators but such that one of the relators is a proper power then G is large. Jack Button has done some work furthering this (he has a paper, from 2008, entitled "Large Groups of Deficiency 1"). But the proper power result is already pretty powerful - it gives you, for instance, that one-relator groups with torsion are Large. | |
| Nov 7, 2011 at 20:58 | comment | added | HJRW | I had in mind the density model of random groups - see the Wikipedia article on random groups. | |
| Nov 7, 2011 at 15:58 | vote | accept | Igor Rivin | ||
| Nov 7, 2011 at 15:58 | comment | added | Igor Rivin | I wonder what "suitable densities" means (obviously I can cook up a density, e.g., supported on free groups, but that's probably not what you have in mind...) | |
| Nov 7, 2011 at 10:23 | comment | added | HJRW | Another relevant fact: Dahmani, Guirardel and Przytycki showed that a random group has property FA, and in particular is not very large. But it's conceivable that, at suitable densities, a random group is large. | |
| Nov 7, 2011 at 10:17 | history | answered | HJRW | CC BY-SA 3.0 |