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.


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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