The problem of freeness for Euler monoids and Möbius groups. (English) Zbl 0980.20038
The authors extend the set of those rational numbers \(\mu\in(-2,2)\) for which the group
\(\Bigl\langle\left(\begin{smallmatrix} 1 &\mu\\ 0 &1\end{smallmatrix}\right),\left(\begin{smallmatrix} 1 &0\\ \mu &1\end{smallmatrix}\right)\Bigr\rangle\) is not free.
\(\Bigl\langle\left(\begin{smallmatrix} 1 &\mu\\ 0 &1\end{smallmatrix}\right),\left(\begin{smallmatrix} 1 &0\\ \mu &1\end{smallmatrix}\right)\Bigr\rangle\) is not free.
Reviewer: Gerhard Rosenberger (Dortmund)
MSC:
| 20H10 | Fuchsian groups and their generalizations (group-theoretic aspects) |
| 20M05 | Free semigroups, generators and relations, word problems |
| 20F05 | Generators, relations, and presentations of groups |
| 20M20 | Semigroups of transformations, relations, partitions, etc. |
