An Aschbacher-O'Nan-Scott theorem for countable linear groups. (Q373862)
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: An Aschbacher-O'Nan-Scott theorem for countable linear groups. |
scientific article; zbMATH DE number 6220112
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An Aschbacher-O'Nan-Scott theorem for countable linear groups. |
scientific article; zbMATH DE number 6220112 |
Statements
An Aschbacher-O'Nan-Scott theorem for countable linear groups. (English)
0 references
25 October 2013
0 references
Let \(\Gamma\) be a countable linear group that admits a faithful primitive action on a set. If \(\Gamma\) is of affine or diagonal type, then this primitive action is uniquely determined (up to isomorphism), [see \textit{T. Gelander} and \textit{Y. Glasner}, Geom. Funct. Anal. 17(2007), No. 5, 1479-1523 (2008; Zbl 1138.20005)]. In the remaining case, \(\Gamma\) is of almost simple type (in the sense of algebraic groups). For this case, the authors construct uncountably many non-isomorphic faithful primitive actions, using a construction from loc. cit.
0 references
countable linear groups
0 references
almost simple algebraic groups
0 references
infinite permutation groups
0 references
faithful primitive actions
0 references
primitive permutation groups
0 references
