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The Quarterly Journal of Mathematics 2004 55(4):463-476; doi:10.1093/qmath/hah015
© 2004 by Oxford University Press
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The power structure of finite p-groups satisfying conditions like those of Lazard

Jon González-Sánchez1 * and Lawrence E. Wilson2 §

1 Departamento de Matemáticas, Facultad de Ciencias, Universidad del País Vasco, Spain, 2 Department of Mathematics, University of Florida, PO Box 118105, 358 Little Hall, Gainesville, FL 32611–8105, USA  *

Lazard proved that finitely generated pro-p groups satisfying {gamma}m(G) ≤ Gph are p-adic analytic if m < ph. Recent work has given a very thorough understanding of the finite p-groups that satisfy this condition with h = 1. In this paper, we consider pro-p groups that show that those results cannot be extended to the case of h = 2 for m ≥ 2p – 1. We do extend many of the results to this case when m ≤ 2p – 3 as well as under some weaker hypotheses.

Received 12 June 2003.

* E-mail: mtbgosaj{at}lg.ehu.es

§ E-mail: larryw{at}math.ufl.edu


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