Abstract
A group in which every element commutes with its endomorphic images is called an E-group. Our main result is that all 3-generator E-groups are abelian. It follows that the minimal number of generators of a finitely generated non-abelian E-group is four.
ACKNOWLEDGMENT
The authors thank the referee for his/her valuable comments for making the article shorter and clearer.
This work was supported partially by the Center of Excellence for Mathematics, University of Isfahan.
The research of the first author was in part supported by a grant from IPM (No. 87200118).
Notes
Communicated by M. R. Dixon.