PRIMITIVITY PRESERVING ENDOMORPHISMS OF FREE GROUPS

Abstract

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.