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Magnus intersections of one-relator free products with small cancellation conditions. (English) Zbl 1170.20018

Summary: D. J. Collins [Lond. Math. Soc. Lect. Note Ser. 311, 255-296 (2004; Zbl 1078.20031)] 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.

MSC:

20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20F05 Generators, relations, and presentations of groups
20F06 Cancellation theory of groups; application of van Kampen diagrams
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)

Citations:

Zbl 1078.20031
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References:

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