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A Magnus theorem for some one-relator groups
Oleg Bogopolski and Konstantin Sviridov
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Geometry & Topology Monographs 14
(2008) 63–73
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Abstract
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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].
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Keywords
fundamental group, normal closure,
amalgamated product
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Mathematical Subject Classification
Primary: 20F34
Secondary: 20E45
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Publication
Received: 29 April 2006
Accepted: 9 November 2006
Published: 29 April 2008
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