2016/05/05 by Benjamin Klopsch, Benno Kuckuck, Klopsch, B. +1
Mathematics · #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.1605.01548
A group G is said to have the Magnus property if the following holds: whenever two elements x,y have the same normal closure, then x is conjugate to y or its inverse. We prove: Let p be an odd prime, and let G,H be residually finite-p groups with the Magnus property. Then the direct product of G and H has the Magnus property. By considering suitable crystallographic groups, we give an explicit example of finitely generated, torsion-free, residually-finite groups G,H with the Magnus property such that the direct product of G and H does not have the Magnus property.