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Nonsingular derivations of modular Lie algebras which have finite multiplicative order play a role in the coclass theory for pro-/? groups and Lie algebras. We study the orders of nonsingular derivations of finite-dimensional non-nilpotent Lie algebras of characteristic p > 0. The methods are essentially number-theoretic.doi:10.1017/s1446788700001208 fatcat:2rdcm5o3qzdi7aumdpucqfnhvu