JournalscmhVol. 76 , No. 2DOI 10.1007/pl00000381

The residual finiteness of positive one-relator groups

  • Daniel T. Wise

    McGill University, Montreal, Canada
The residual finiteness of positive one-relator groups cover

Abstract

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.