The residual finiteness of positive one-relator groups

  • Daniel T. Wise

    McGill University, Montreal, Canada


It is proven that every positive one-relator group which satisfies the C(16){\rm C}'({1\over6}) 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(16){\rm C}'({1\over6}) positive one-relator group is residually finite. It is shown that positive one-relator groups are generically C(16){\rm C}'({1\over6}) and hence generically residually finite. A new method is given for recognizing malnormal subgroups of free groups. This method employs a 'small cancellation theory' for maps between graphs.

Cite this article

Daniel T. Wise, The residual finiteness of positive one-relator groups. Comment. Math. Helv. 76 (2001), no. 2, pp. 314–338

DOI 10.1007/PL00000381