On a theorem of Zelmanov (Q1818875)
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: On a theorem of Zelmanov |
scientific article; zbMATH DE number 1384480
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a theorem of Zelmanov |
scientific article; zbMATH DE number 1384480 |
Statements
On a theorem of Zelmanov (English)
0 references
5 September 2000
0 references
The author gives a new (more direct and short) proof of the result of Zelmanov that a non-cyclic pro-\(p\) group \(G\) satisfying the Golod-Shafarevich inequality contains a nonabelian free pro-\(p\) subgroup. It is proved in addition that a quotient group of \(G\) contains a closed normal subgroup which is a Cartesian product of infinitely many finitely generated infinite pro-\(p\) groups, each of which is an epimorphic image of an open normal subgroup of \(G\).
0 references
pro-\(p\) groups
0 references
free pro-\(p\) subgroups
0 references
closed normal subgroups
0 references
open normal subgroups
0 references
