JournalslemVol. 58, No. 1/2pp. 49–60

Alternating quotients of free groups

  • Henry Wilton

    University of Cambridge, Great Britain
Alternating quotients of free groups cover
Download PDF


We strengthen Marshall Hall's theorem to show that free groups are locally extended residually alternating. Let FF be any free group of rank at least two, let~HH be a finitely generated subgroup of infinite index in FF and let {γ1,,γn}FH\{\gamma_1,\ldots,\gamma_n\}\subseteq F\smallsetminus H be a finite subset. Then there is a surjection ff from FF to a finite alternating group such that f(γi)f(H)f(\gamma_i)\notin f(H) for any ii. 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. 49–60

DOI 10.4171/LEM/58-1-2