Non-free two-generator subgroups of \(\text{SL}_ 2(\mathbb{Q})\) (Q1915431)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Non-free two-generator subgroups of \(\text{SL}_ 2(\mathbb{Q})\) |
scientific article; zbMATH DE number 889857
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Non-free two-generator subgroups of \(\text{SL}_ 2(\mathbb{Q})\) |
scientific article; zbMATH DE number 889857 |
Statements
Non-free two-generator subgroups of \(\text{SL}_ 2(\mathbb{Q})\) (English)
0 references
27 October 1996
0 references
A classical question is whether two given parabolic elements \(A,B\in\text{SL}(2,\mathbb{C})\) generate freely a free group or not. This reduces to the question for which values of \(z=\text{tr}(AB)\) the group generated by \(A\) and \(B\) is free of rank two or not. There are many known partial results but we have no general final answer for this question. Here we find a collection of such values \(z\) for which the corresponding group is non-free.
0 references
parabolic elements
0 references
free groups
0 references
