Free Subgroups of Linear Groups

Abstract

Note that from the definition immediately follows that the group G is a free group with free generators gi, i ∈ I. Indeed, let g = g1 i1 . . . g mk ik be any reduced word. Take p ∈ D0, then gp ∈ D± i1 ⊆ H2 \D0. Therefore g 6= 1. One of the main purposes of the present work is to show how the beautiful ideas of Tits were developed in our joint works with G. Margulis [MS1], [MS2], [MS3]. Our interest to free subgroups of linear groups was initiated by the following Problem 1 (V. Platonov) Does there exist a maximal subgroup of infinite index