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

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Abstract

A study of the set \( \mathcal{N}_p \) 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 produce more elements of \( \mathcal{N}_p \). Our main result shows that any divisor n of q − 1, where q is a power of p, such that n ≥ (p − 1)1/p(q − 1)1−1/(2p), necessarily belongs to \( \mathcal{N}_p \). This extends its special case for p = 2 which was proved in a previous paper by a different method.

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  1. Dipartimento di Matematica, Università degli Studi di Trento, via Sommarive 14, I-38050, Povo (Trento), Italy

    S. Mattarei

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  1. S. Mattarei
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Correspondence to S. Mattarei.

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Mattarei, S. A sufficient condition for a number to be the order of a nonsingular derivation of a Lie algebra. Isr. J. Math. 171, 1–14 (2009). https://doi.org/10.1007/s11856-009-0036-7

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  • DOI: https://doi.org/10.1007/s11856-009-0036-7

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