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, xy› 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