JournalsggdVol. 1 , No. 4DOI 10.4171/ggd/23

Magnus intersections of one-relator free products with small cancellation conditions

  • Arye Juhász

    Technion - Israel Institute of Technology, Haifa, Israel
Magnus intersections of one-relator free products with small cancellation conditions cover

Abstract

Donald Collins initiated the study of intersections of Magnus subgroups in one-relator groups. In particular, he characterized those intersections of Magnus subgroups that are not Magnus subgroups. In the present work we show that Collins’ results extend to one-relator quotients of free products of groups with a small cancellation condition and give a complete list of those defining relators for which Magnus subgroups do not intersect in a Magnus subgroup. We use van Kampen diagrams and word combinatorics.