Primitive finitary skew linear groups
We discuss normal subgroups \(N\) of primitive subgroups \(G\) of the finitary general linear group \(FLG(V)\) of any vector space \(V\) over any division ring \(D\). Usually we assume some solubility restriction on \(N\). As a corollary of our main result we have the following. Let \(G\) be a primitive irreducible subgroup of \(FGL(V)\). If either, \(G\) is hyper locally nilpotent (that is radical in the sense of Kurosh), or, \(G\) is locally soluble and \(D\) is locally finite-dimensional over its centre, then \(V\) has finite dimension over \(D\).
scientific article; zbMATH DE number 590066