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Results tagged with gr.group-theory
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user 8381
Questions about the branch of algebra that deals with groups.
3
votes
1
answer
197
views
Properties of quantum torus group
Let $G = \langle x,y,q ~|~ xy=qyx,~ qx = xq,~ qy=yq\rangle$ is an abstract group.
1) Does this group have a common name? ("quantum tori" is the name of a certain related algebra)
2) What properties …
- 1,278
3
votes
Deriving a relation in a group based on a presentation
It's a bit late answer, but there is a nice proof :).
Denote $t = x^3 = y^5$, so $t$ is in center of $G$. Add new symbol $u$ and state that it commutes with other symbols and $u^{-30}=t$, so we obtain …
- 1,278
4
votes
Torsion in triangle groups
Also you can reference to theorem 2.10 in W.Magnus "Noneuclidean Tesselations and Their Groups" ACADEMIC PRESS New York 1974.
- 1,278
4
votes
3
answers
443
views
Ways to prove an inequality in groups
Suppose we have a (possibly infinite) group given by generators and relations. One way to prove some inequality is to construct the representation of the group and show inequality in the representatio …
- 1,278
2
votes
1
answer
342
views
Presentations of infinite index subgroups
Suppose we have a finitely presented group $G$ with a concrete presentation and a subgroup $H$, generated by a finite set of elements from $G$. How to find the presentation for $H$?
If $H$ has finite …
- 1,278
38
votes
7
answers
9k
views
Bijection between irreducible representations and conjugacy classes of finite groups
Is there some natural bijection between irreducible representations and conjugacy classes of finite groups (as in case of $S_n$)?
- 1,278