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ABSTRACT
An endomorphism of a free group is called primitivity preserving if
takes every primitive element to another primitive. In this paper we prove that every primitivity preserving endomorphism of a free group of a finite rank
is an automorphism.
ACKNOWLEDGMENTS
The author is greatly indebted to Professor Sergei V. Ivanov for his valuable advice and kind encouragement. The author also thanks the referee for the helpful comments and suggestions.