## The residual finiteness of positive one-relator groups.(English)Zbl 1023.20011

From the summary: It is proven that every positive one-relator group which satisfies the $$C'(\tfrac 16)$$ condition has a finite index subgroup which splits as a free product of two free groups amalgamating a finitely generated malnormal subgroup. As a consequence, it is shown that every $$C'(\tfrac 16)$$ positive one-relator group is residually finite. It is shown that positive one-relator groups are generically $$C'(\tfrac 16)$$ and hence generically residually finite.

### MSC:

 20E26 Residual properties and generalizations; residually finite groups 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
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