3-Generator Groups whose Elements Commute with Their Endomorphic Images Are Abelian

Abdollahi, A.; Faghihi, A.; Hassanabadi, A. Mohammadi

3-Generator Groups whose Elements Commute with Their Endomorphic Images Are Abelian

Authors

Abdollahi, A.

Faghihi, A.

Hassanabadi, A. Mohammadi

Description

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.