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 Yearling
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Apr
18
revised Is the map $\phi(r+4 \mathbb{Z})=r^3 + 4\mathbb{Z}$ well defined?
Improved title to describe question, removed irrelevant tag (this question is not about mapping class groups)
Apr
18
revised Isomorphism between Frac($\mathbb Z[x]$) and Frac($\mathbb Q[x]$)
Does not seem to be about mapping class groups
Apr
14
awarded  Yearling
Apr
9
comment Is the Cayley graph of a word-hyperbolic group a CAT(0) metric space?
I edited the Wikipedia page, and edited the link on this question to go to the old version to preserve the question (just letting future people who see this question know).
Apr
9
revised Is the Cayley graph of a word-hyperbolic group a CAT(0) metric space?
Since the statement on Wikipedia is wrong, I changed it, and edited the link to the old version which this question is about, to preserve this question.
Apr
8
comment Is the Cayley graph of a word-hyperbolic group a CAT(0) metric space?
It looks like a mistake, I looked at the history and it used to say cayley graph of discrete groups, which is certainly not true, and I guess the person who corrected that ended up inserting a more subtle error, although it is a well known open problem if hyperbolic groups are CAT(0) (note there is no reference to the claim).
Apr
7
comment A problem in hyperbolic group
Are the $x_i$ arbitrary generators (or from the symmetric generating set), and is $n$ the length of $x$, or is it some initial segment of $x$? Also where did you see this?
Apr
7
revised A problem in hyperbolic group
Improved formatting
Mar
25
comment Looking for references on infinite groups
There is nothing to say, as it essentially boils down to just "what can I derive from just the group axioms" (which is basically just trivial things). Also the statement that is attributed to Gromov was actually in reference to finitely generated groups (maybe even finitely presented groups), so even in the finitely generated case there is not much to say.
Mar
18
comment Order $n$ elements of infinite groups of finite exponent $n>2$
@Marc My answer is flawed, could you unaccept it so I can delete it? (It assumes there are elements of order equal to the exponent, and the last part about infinitely many $g_1h_ih_j^{-1}$ of order $n$ is not as clear as I thought it was when writing it)
Mar
16
comment The definition of the number of ends for a locally finite graph
You should add some context, like where did you see this definition mentioned?
Mar
1
comment Subgroups of an infinite group with a given index
In remark towards the end of the paper, Shelah says that it could be done with $\aleph_2$ (without CH), but for further $\aleph_n$ the situation not clear. @TobiasKildetoft
Mar
1
comment Subgroups of an infinite group with a given index
@TobiasKildetoft Actually for the $\aleph_1$ case it does not depend on the continuum hypothesis. (It does not rely on whether or not $\aleph_1=2^{\aleph_0}$)
Mar
1
comment Subgroups of an infinite group with a given index
@DustanLevenstein The paper proves that there are Johnsson groups of cardinality $\aleph_1$, and of cardinality $\lambda^+$ when $\lambda^+=2^\lambda$. I am not sure if there is a reason why it could not be for arbitrary cardinalities though (maybe there is a general obstruction).
Mar
1
revised Subgroups of an infinite group with a given index
added 44 characters in body
Mar
1
answered Subgroups of an infinite group with a given index
Feb
26
comment The graph of free product group.
Maybe if you add more about what you don't understand, someone could answer it.
Feb
26
comment The graph of free product group.
What about it do you not understand?(Have you tried an example, like $C_2*C_3$ or something) Your question is very vague and broad. Also you should try your best to actually ask your question the first time, and edit to improve (instead of completely changing it), and this is why context in questions is so important, so that people actually know what is your problem and what you are talking about. For what it is worth I think you are talking about trees which come out of Bass-Serre theory.
Feb
26
comment The graph of free product group.
Okay, I now see the question has completely changed...
Feb
26
comment The graph of free product group.
I actually dont think 6666 is looking for the cayley graph, looks more like a Bass-Serre tree