Groups, Geometry, and Dynamics


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Volume 1, Issue 4, 2007, pp. 421–468
DOI: 10.4171/GGD/21

Published online: 2007-12-31

A partial extension of Lazard's correspondence for finite p-groups

George Glauberman[1]

(1) University of Chicago, United States

M. Lazard established a correspondence between finite p-groups of nilpotence class less than p and finite nilpotent Lie rings of p-power order and nilpotence class less than p. This correspondence has had many applications, but cannot generally be extended to p-groups of class p or larger. However, in this paper, we obtain a partial extension of Lazard's result for a p-group that is a product of normal subgroups of class less than p.

Keywords: Finite p-groups, Lie algebras

Glauberman George: A partial extension of Lazard's correspondence for finite p-groups. Groups Geom. Dyn. 1 (2007), 421-468. doi: 10.4171/GGD/21