# Rendiconti del Seminario Matematico della Università di Padova

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**Volume 124, 2010, pp. 139–144**

**DOI: 10.4171/RSMUP/124-8**

Published online: 2010-12-31

Periodic-by-Nilpotent Linear Groups

B.A.F. Wehrfritz^{[1]}(1) Queen Mary University of London, UK

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.

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Wehrfritz B.A.F.: Periodic-by-Nilpotent Linear Groups. *Rend. Sem. Mat. Univ. Padova* 124 (2010), 139-144. doi: 10.4171/RSMUP/124-8