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.
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Arye Juhász, Magnus intersections of one-relator free products with small cancellation conditions. Groups Geom. Dyn. 1 (2007), no. 4, pp. 525–552DOI 10.4171/GGD/23