bio | website | dpmms.cam.ac.uk/~hjrw2 |
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location | Cambridge | |
age | ||
visits | member for | 5 years, 2 months |
seen | 7 hours ago | |
stats | profile views | 5,844 |
Jan 11 |
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Two groups that are the automorphism groups of each other
Having said that, Joel David Hamkins does write in a comment 'I believe that no examples are known with period 2 or larger.' But I think he may be talking about 'strong' isomorphism (ie insisting that the isomorphisms are the maps that send elements to inner automorphisms). |
Jan 11 |
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Two groups that are the automorphism groups of each other
Sorry, I was too hasty. I meant for the finite case with no centre. |
Jan 10 |
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Two groups that are the automorphism groups of each other
I think this question is answered in the comments to this question: mathoverflow.net/questions/5635/… |
Jan 9 |
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Is this statement true?
Since this question is not research-level, I'm voting to close. |
Jan 7 |
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Non-abelian Grothendieck group
Wait, my mistake - apologies. |
Jan 7 |
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Non-abelian Grothendieck group
The group still seems to be free, since the relations just say that some generator is equal to a product of other relators. |
Jan 7 |
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Conjugates and infinite index subgroups of free groups
It generalizes to hyperbolic groups and quasiconvex subgroups. |
Jan 7 |
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Exotic actions of hyperbolic groups
that seems plausible. Of course, your question would then be equivalent to a famous open problem. |
Jan 7 |
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Conjugates and infinite index subgroups of free groups
@Pablo, a finite Stallings graph represents an infinite-index subgroup iff some vertex has less than maximal degree. |
Jan 7 |
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Are there quasiconvex normal subgroups?
Of course. But he did it before hyperbolic groups had been invented, and probably phrased his proof differently. I haven't looked at his paper. |
Jan 7 |
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Are there quasiconvex normal subgroups?
@Igor, he did Fuchsian groups. |
Jan 7 |
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Exotic actions of hyperbolic groups
Could you give an example of such an action when $G$ is free? |
Jan 7 |
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Exotic actions of hyperbolic groups
Algebraically, what does the highly transitive hypothesis mean about a point stabilizer? |
Jan 7 |
answered | Are there quasiconvex normal subgroups? |
Jan 6 |
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Growth of the number of generators in hyperbolic groups
@Pablo, all I meant was that, for a fi subgroup H of a 2-dimensional group G, $b_1(H) \geq 1-|G:H|\chi(G)$, by the multiplicativity of Euler characteristic. Thanks for your e-mail - I'll reply soon! |
Jan 5 |
awarded | Enlightened |
Jan 5 |
awarded | Nice Answer |
Jan 4 |
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Is residual finiteness a property of “many” finitely presented groups?
Pablo, this is also a good question. Do you want to send me an e-mail? |
Jan 4 |
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Is residual finiteness a property of “many” finitely presented groups?
(But you might like to check out the work of Sapir and his co-authors on random 1-relator groups with more generators.) |
Jan 4 |
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Is residual finiteness a property of “many” finitely presented groups?
Pablo, I think this is an interesting question. The result I mentioned about 2-generator 1-relator groups is in a paper of Dunfield and (Dylan) Thurston. They prove that a random 2-generator 1-relator group is fg-free-by-cyclic with probability strictly between 0 and 1. In particular, at least some of the time, such groups have zero rank gradient. As far as I know, nothing is known about models with more generators or relations. |