Free subgroups in linear groups

Abstract

(i) H contains no non-abelian free group. (ii) G has a solvable normal subgroup R such that G,‘R is locally .fnite (i.e., every jinite subset generates a$nite subgroup). (iii) G possesses a subgroup G’ of finite index such that if V’ denotes any composition factor of the k[G’]-module V and k’ the endomorphism ring of V’ (i.e., the centralizer of G’ in End,L V’), then k’ is a jield and V’ has a k’-basis with respect to which the matrices representing the elements of G’ are scalar multiples (by elements of k’) f o matrices whose entries are algebraic over the prime field of k.