Abstract.
In this paper we obtain a local limit theorem for elements of a free group G under the abelianization map \([\cdot] :G \to G/[G,G]\). This is obtained via an analysis involving subshifts of finite type, where we obtain a result of independent interest. The case of fundamental groups of compact surfaces of genus \(\geq 2\) is also discussed.
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Received: 20 December 2000 / Revised version: 23 March 2001 / Published online: 24 September 2001
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Sharp, R. Local limit theorems for free groups. Math Ann 321, 889–904 (2001). https://doi.org/10.1007/s002080100258
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DOI: https://doi.org/10.1007/s002080100258