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Apr
10
comment Free Groups and Automatic Structures
Also, let me add that since Mathoverflow (where this question was first posted) is by definition concerned with questions about research-level mathematics, I would (friendlily!) encourage non-mathematicians to start by posting their question on math.SE. Of course, if your question doesn't get an answer there, then trying MO is entirely appropriate.
Apr
10
comment Free Groups and Automatic Structures
In that case I would encourage you to include the reading that you have done in the question. If you state that you've read 'Word processing in groups', say, but you're still confused about something, and can explain what that thing is, then you're more likely to get a helpful answer.
Apr
9
comment Free Groups and Automatic Structures
Derek's answer is great, but this is surely contained in the standard book on the subject (eg Word Processing in Groups). I'm voting to close - MO is not a lazy alternative to reading the literature.
Mar
6
comment Fundamental group of row of spheres
Please, let's not post answers to questions which are clearly off-topic.
Feb
25
revised Finding subgroups of a free group with a specific index
Corrected a typo in Hall's formula.
Feb
3
comment Is there any connected n-manifold such that $H_n(X,Z)=Z\times Z$?
@lanse2pty, any closed $n$-submanifold is clopen.
Nov
21
comment Covering Manifolds
I always think of 'the Disc Theorem' as the conjunction of the Loop Theorem and Dehn's Lemma.
Nov
21
comment Covering Manifolds
a) is obvious (ie not MO-level). b) is a consequence of the loop theorem, as already explained in the comments.
Nov
17
comment Product in an non-commutative group
By the way, you might be interested to notice that any group which does have your property is commutative, because $ghg^{-1}h^{-1}=gg^{-1}hh^{-1}=1$ for any $g,h$.
Nov
17
answered Product in an non-commutative group
Oct
31
comment Given probability of event
(Note: the above comment was written when this question and answer were posted on mathoverflow.)
Oct
31
comment Given probability of event
Please don't answer questions that are not at research-level. They're off topic at MO. They can be migrated to math.stackexchange, where they are on topic and can be answered appropriately.
Oct
21
comment Universal Covering Space
@t.b. , your idea is not the right way to construct the universal cover, but it is useful and interesting! If $X$ is a graph, say, then your limit $\varprojlim X_n$ is a profinite tree, and the profinite fundamental group of $X$, which is a free profinite group, acts on it. Ribes and Zalesskii have developed a very nice theory of profinite trees.
Oct
3
awarded  Yearling
Aug
5
awarded  Nice Answer
Jul
25
comment Easy explanation of non-abelianness of hyperbolic curves
Misha - I agree. I was just hoping that the OP would find this helpful.
Jul
25
comment Easy explanation of non-abelianness of hyperbolic curves
Here, $\Sigma_g$ is of course the closed surface of genus $g$. Since non-closed surfaces have free fundamental groups, the arguments in those cases are even easier.
Jul
25
answered Easy explanation of non-abelianness of hyperbolic curves
Dec
18
awarded  Nice Answer
Oct
3
awarded  Yearling