Soluble normal subgroups of skew linear groups
Let P(U\(\cup LF)\) be the class of all groups with a normal series of finite length whose factors are abelian or locally finite. Let D be a division ring, \(D^{n\times n}\) the matrix ring of degree n over D and GL(n,D) the group of units of \(D^{n\times n}\). Let F be a centre of D. A group \(G\subset GL(n,D)\) is called absolutely irreducible if the F- enveloping algebra of G in \(D^{n\times n}\) coincides with \(D^{n\times n}.\) The main result of this article is the following theorem: Let \(G\subset GL(n,D)\) be an absolutely irreducible group and H a normal P(U\(\cup LF)\)- subgroup of G. (i) H contains an abelian normal subgroup A of G with H/A locally finite and \(G/C_ G(H)\) is abelian by periodic; (ii) if H modulo its centre is periodic then \(G/C_ G(H)\) is periodic.
scientific article; zbMATH DE number 3975224
scientific article