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Results tagged with gr.group-theory
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user 6429
Questions about the branch of algebra that deals with groups.
23
votes
1
answer
3k
views
Finitely presented infinite group with no element of infinite order?
Is there an example of a finitely presented infinite group in which every element has finite order? Or, is it known that every finitely presented infinite group has an element of infinite order?
I as …
- 726
1
vote
1
answer
210
views
Equivalent conditions for coHopfian groups
A lot of work has been done on determining whether particular classes of groups are coHopfian, in particular the (sufficiently large) braid groups $B_n$ modulo center, and certain classes of 3-manifol …
- 726
10
votes
2
answers
686
views
Freiheitssatz implies a finitely generated one relator group embeds in a two-generator one r...
I've read that every finitely generated one relator group embeds in a two generator one relator group, and that this fact follows from the Freiheitssatz.
Unfortunately, the only proof I can find of …
- 726
3
votes
1
answer
326
views
Does the group given by this presentation have an element of order 2?
Suppose $G$ has the presentation $\langle t, x_1, x_2, ... | R \rangle$ where each relator in $R$ has the form $t^{-1}x_it = x_j$ for some $i,j$. Does $G$ have an element of order 2?
This is an HNN e …
- 726
1
vote
1
answer
156
views
Sufficient Conditions for Free Indecomposability
An interesting fact was relayed to me in another question of mine that
If $M$ is any closed manifold with universal cover homeomorphic to $R^n$ for $n>1$ then $\pi_1(M)$ is freely indecomposable. …
- 726