A Magnus theorem for some amalgamated products. Issue 12 (2nd December 2019)

• Record Type: Journal Article
• Authors: Feldkamp, Carsten
• Is Part Of: Communications in algebra. Volume 47:Issue 12(2019)
• Page Start: 5348
• Page End: 5360
• Publication Date: 2019-12-02
• Subjects: Group Theory -- Magnus property -- amalgamated products -- surface groups; 20E06; 20E45; 20F05; 20F34; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1623235
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: A group G possesses the Magnus property if for every two elements u, v ∈ G with the same normal closure, u is conjugate in G to v or v − 1 . We prove the Magnus property for some amalgamated products including the fundamental group of a closed non-orientable surface of genus 3. This answers a question of O. Bogopolski and K. Sviridov, who obtained the analogous result for genus g > 3.