Alternating quotients of free groups
Group Theory
2011-12-12 v2 Geometric Topology
Abstract
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 {g_1,...,g_n} be a finite subset of F-H. Then there is a surjection f from F to a finite alternating group such that f(g_i) is not in f(H) for any i. The techniques of this paper can also provide symmetric quotients.
Keywords
Cite
@article{arxiv.1005.0015,
title = {Alternating quotients of free groups},
author = {Henry Wilton},
journal= {arXiv preprint arXiv:1005.0015},
year = {2011}
}
Comments
11 pages, 5 figures. Referee's comments incorporated. To appear in L'Enseignement Math\'ematique