JournalslemVol. 58, No. 1/2pp. 49–60

Alternating quotients of free groups

  • Henry Wilton

    University of Cambridge, Great Britain
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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. 1/2, pp. 49–60

DOI 10.4171/LEM/58-1-2