Alternating quotients of free groups

Details Alternating quotients of free groups Alternating quotients of free groups

2010-04-30

arxiv.org/abs/1005.0015v2

Mathematics

Group Theory

11 pages, 5 figures. Referee's comments incorporated. To appear in L'Enseignement Math\'ematique

Scientific paper

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.

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