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arXiv · 0706.1810

A sufficient condition for a number to be the order of a nonsingular derivation of a Lie algebra

Sandro Mattarei
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Abstract

A study of the set N_p of positive integers which occur as orders of nonsingular derivations of finite-dimensional non-nilpotent Lie algebras of characteristic p>0 was initiated by Shalev and continued by the present author. The main goal of this paper is to show the abundance of elements of N_p. Our main result shows that any divisor n of q-1, where q is a power of p, such that $n\ge (p-1)^{1/p} (q-1)^{1-1/(2p)}$, belongs to N_p. This extends its special case for p=2 which was proved in a previous paper by a different method.

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Sandro Mattarei. 2007-10-17. A sufficient condition for a number to be the order of a nonsingular derivation of a Lie algebra. https://doi.org/10.1007/s11856-009-0036-7

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