We will say that a group G possesses the Magnus property if for
any two elements u,v∈ 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
