Alternating quotients of free groups

  • Henry Wilton

    University of Cambridge, Great Britain


We strengthen Marshall Hall's theorem to show that free groups are locally extended residually alternating. Let be any free group of rank at least two, let be a finitely generated subgroup of infinite index in and let be a finite subset. Then there is a surjection from to a finite alternating group such that for any . The techniques of this paper can also provide symmetric quotients.

Cite this article

Henry Wilton, Alternating quotients of free groups. Enseign. Math. 58 (2012), no. 1/2, pp. 49–60

DOI 10.4171/LEM/58-1-2