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A Magnus theorem for some one-relator groups

Oleg Bogopolski and Konstantin Sviridov

Geometry & Topology Monographs 14 (2008) 63–73

DOI: 10.2140/gtm.2008.14.63

arXiv: 0904.1143

Abstract

We will say that a group G possesses the Magnus property if for any two elements u,v in G with the same normal closure, u is conjugate to v or v-1. We prove that some one-relator groups, including the fundamental groups of closed nonorientable surfaces of genus g>3 possess this property. The analogous result for orientable surfaces of any finite genus was obtained by the first author [Geometric methods in group theory, Contemp. Math, 372 (2005) 59-69].

Keywords

fundamental group, normal closure, amalgamated product

Mathematical Subject Classification

Primary: 20F34

Secondary: 20E45

References
Publication

Received: 29 April 2006
Accepted: 9 November 2006
Published: 29 April 2008

Authors
Oleg Bogopolski
Fachbereich Mathematik
Universität Dortmund
Vogelpothsweg 87
Dortmund, 44227
Germany
http://www.mathematik.uni-dortmund.de/lsvi/bogopolski/index.html
Konstantin Sviridov
Institute of Mathematics of SBRAS
Koptjuga 4
Novosibirsk, 630090
Russia