Periodic-by-Nilpotent Linear Groups

Abstract

Let G be a linear group of (finite) degree n and characteristic p ≥ 0. Suppose that for every infinite subset X of G there exist distinct elements x and y of X with ‹x, x__y› periodic-by-nilpotent. Then G has a periodic normal subgroup T such that if p > 0 then G/T is torsion-free abelian and if p = 0 then G/T is torsion-free nilpotent of class at most max{1, _n_−1} and is isomorphic to a linear group of degree n and characteristic zero. We also discuss the structure of periodic-by-nilpotent linear groups.