# 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 $max1,n−1$ 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