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, pp. 49–60DOI 10.4171/LEM/58-1-2