Gelander, Tsachik; Glasner, Yair An Aschbacher-O’Nan-Scott theorem for countable linear groups. (English) Zbl 1285.20002 J. Algebra 378, 58-63 (2013). 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 T. Gelander and 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. Reviewer: Theo Grundhöfer (Würzburg) Cited in 3 Documents MSC: 20B07 General theory for infinite permutation groups 20G15 Linear algebraic groups over arbitrary fields 20B15 Primitive groups Keywords:countable linear groups; almost simple algebraic groups; infinite permutation groups; faithful primitive actions; primitive permutation groups Citations:Zbl 1138.20005 PDFBibTeX XMLCite \textit{T. Gelander} and \textit{Y. Glasner}, J. Algebra 378, 58--63 (2013; Zbl 1285.20002) Full Text: DOI arXiv Link