On absolutely irreducible skew linear groups in characteristic zero
Let H be a locally finite normal subgroup of an absolutely irreducible skew linear group. In an earlier paper [J. Lond. Math. Soc., II. Ser. (to appear; Zbl 0545.20040)] we proved that the structure of G modulo the centralizer \(C_ G(H)\) is very restricted, especially in the positive characteristic case. Here we study further the more involved characteristic zero case. The paper quoted above showed that \(G/C_ G(H)\) is metabelian by finite and locally finite but need not be locally-nilpotent by finite. In particular this holds if \(G=H\) so the possibility naturally arises that \(G/HC_ G(H)\) has a simpler structure. We show that \(G/HC_ G(H)\) is abelian by finite and residually finite.
absolutely irreducible skew linear group
scientific article; zbMATH DE number 3865583