Golod-Shafarevich groups with property \((T)\) and Kac-Moody groups. (Q955157)
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: Golod-Shafarevich groups with property \((T)\) and Kac-Moody groups. |
scientific article; zbMATH DE number 5368505
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Golod-Shafarevich groups with property \((T)\) and Kac-Moody groups. |
scientific article; zbMATH DE number 5368505 |
Statements
Golod-Shafarevich groups with property \((T)\) and Kac-Moody groups. (English)
0 references
18 November 2008
0 references
A pro-\(p\) group \(G\) is called Golod-Shafarevich if it has a pro-\(p\) presentation satisfying a certain condition which guarantees that \(G\) is infinite. Such groups appear as Galois groups and also in 3-dimensional geometry. The main result is that for every sufficiently large prime \(p\) there is a finitely generated group with \(T\)-propertry whose pro-\(p\) completion is Golod-Shafarevich. This refutes a recent conjecture of Zelmanov.
0 references
T-property
0 references
Golod-Shafarevich condition
0 references
Golod-Shafarevich groups
0 references
pro-\(p\) groups
0 references
pro-\(p\) presentations
0 references
pro-\(p\) completions
0 references
0 references
0 references
