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

摘要

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.View full textDownload full textKey Words2-Engel groups, Endomorphisms of groups, Near-rings, p-Groups2000 Mathematics Subject Classification20D45, 20E36Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927870802160727