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

Juhász, Arye

doi:10.4171/GGD/23

Groups, Geometry, and Dynamics

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Volume 1, Issue 4, 2007, pp. 525–552

DOI: 10.4171/GGD/23

Published online: 2007-12-31

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

Arye Juhász^[1]

(1) Technion - Israel Institute of Technology, Haifa, Israel

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.

Keywords: One-relator free products, small cancellation theory, word-combinatorics, Magnus subgroups

Juhász Arye: Magnus intersections of one-relator free products with small cancellation conditions. Groups Geom. Dyn. 1 (2007), 525-552. doi: 10.4171/GGD/23