most recent 30 from http://mathoverflow.net 2013-05-24T10:22:05Z http://mathoverflow.net/feeds/user/4682 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/18423/proving-that-a-group-is-free Nick Hildebrand 2010-03-16T20:56:11Z 2010-05-11T15:56:03Z

<p>I've got a group $G$ that I'm trying to prove is free. I already know that $G$ is torsion-free. Moreover, I can "almost" prove what I want : I can find a finite index subgroup $G'$ of $G$ that is definitely free.</p> <p>This leads me to the following question. Can anyone give me an example of a torsion-free group $G$ that is not free but contains a free subgroup of finite index? I've tried pretty hard to find groups like this, but i can't seem to avoid introducing torsion. Thanks!</p>

http://mathoverflow.net/questions/20539/decidability-of-conjugacy-problem-for-finitely-generated-subgroups-of-free-groups Nick Hildebrand 2010-04-06T19:41:25Z 2010-04-16T16:38:14Z

<p>The conjugacy problem for a free group $F_n$ on $n$ letters has an easy solution. Each element of $F_n$ is conjugate to a unique and easily computable "cyclically reduced element" (this means that if you arrange the word around a circle, then there are no cancellations), so two elements of $F_n$ are conjugate if and only if they have the same cyclically reduced conjugates.</p> <p>I've been trying unsuccessfully to generalize this to solve the following problem. Let ${x_1,\ldots,x_k}$ and ${y_1,\ldots,y_{k'}}$ be two finite sets of elements of $F_n$. Let $G_x$ and $G_y$ be the subgroups of $F_n$ generated by the $x_i$ and the $y_i$, respectively. Is there an algorithm to decide if $G_x$ and $G_y$ are conjugate? Does anyone know how to do this? Thank you very much!</p>

http://mathoverflow.net/questions/20471/why-are-free-groups-residually-finite/20488#20488 Nick Hildebrand 2010-04-06T19:15:47Z 2010-04-06T19:15:47Z

Doesn't this proof generalize to give Malcev's theorem? The proof I know for finitely generated linear groups over fields goes along these same lines. I'm not sure about finitely generated linear groups over arbitrary commutative rings.

http://mathoverflow.net/questions/18423/proving-that-a-group-is-free/18425#18425 Nick Hildebrand 2010-03-16T22:31:04Z 2010-03-16T22:31:04Z

Thank you very much! Given the people whose work you had to use to prove this, I don't feel so bad for not being able to do it myself =)

http://mathoverflow.net/questions/18423/proving-that-a-group-is-free/18424#18424 Nick Hildebrand 2010-03-16T21:07:51Z 2010-03-16T21:07:51Z

Isn't Z+0 infinite index? The quotient is Z, which is an infinite group.