Geodesic
An endomorphism of a~free Lie algebra that preserves the property of primitiveness of elements is an automorphism
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 48 (1993) no. 6, pp. 189-190

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     author = {A. A. Zolotykh and A. A. Mikhalev},
     title = {An endomorphism of a~free {Lie} algebra that preserves the property of primitiveness of elements is an automorphism},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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A. A. Zolotykh; A. A. Mikhalev. An endomorphism of a~free Lie algebra that preserves the property of primitiveness of elements is an automorphism. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 48 (1993) no. 6, pp. 189-190. http://geodesic.mathdoc.fr/item/RM_1993_48_6_a20/