# Periodic-by-Nilpotent Linear Groups

### B.A.F. Wehrfritz

Queen Mary University of London, UK

## 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.

## Cite this article

B.A.F. Wehrfritz, Periodic-by-Nilpotent Linear Groups. Rend. Sem. Mat. Univ. Padova 124 (2010), pp. 139–144

DOI 10.4171/RSMUP/124-8