Alternating quotients of free groups

2010/04/30 by Wilton, Henry
#20E05 #20E26 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1005.0015

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 g₁,...,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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