The orders of nonsingular derivations

Nonsingular derivations of modular Lie algebras which have finite multiplicative order play a role in the coclass theory for pro-pgroups and Lie algebras. We study the orders of nonsingular derivations of finite-dimensional non-nilpotent Lie algebras of characteristicp> 0. The methods are essentially number-theoretic. 1991Mathematics subject classification (Amer. Math. Soc): primary 17B50; secondary 12E20.