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L’Enseignement Mathématique

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Volume 58, Issue 1/2, 2012, pp. 49–60
DOI: 10.4171/LEM/58-1-2

Published online: 2012-06-30

Alternating quotients of free groups

Henry Wilton[1]

(1) University of Cambridge, Great Britain

We strengthen Marshall Hall's theorem to show that free groups are locally extended residually alternating. Let $F$ be any free group of rank at least two, let~$H$ be a finitely generated subgroup of infinite index in $F$ and let $\{\gamma_1,\ldots,\gamma_n\}\subseteq F\smallsetminus H$ be a finite subset. Then there is a surjection $f$ from $F$ to a finite alternating group such that $f(\gamma_i)\notin f(H)$ for any $i$. The techniques of this paper can also provide symmetric quotients.

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Wilton Henry: Alternating quotients of free groups. Enseign. Math. 58 (2012), 49-60. doi: 10.4171/LEM/58-1-2