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Hall’s Theorem for Limit Groups

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Abstract.

A celebrated theorem of Marshall Hall Jr. implies that finitely generated free groups are subgroup separable and that all of their finitely generated subgroups are retracts of finite-index subgroups. We use topological techniques inspired by the work of Stallings to prove that all limit groups share these two properties. This answers a question of Sela.

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Authors and Affiliations

  1. Department of Mathematics, 1 University Station C1200, Austin, TX, 78712-0257, USA

    Henry Wilton

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  1. Henry Wilton
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Correspondence to Henry Wilton.

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Partially supported by an EPSRC student scholarship and by a post-doctoral fellowship at the Hebrew University of Jerusalem, Israel.

Received: May 2006 Revision: May 2007 Accepted: May 2007

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Wilton, H. Hall’s Theorem for Limit Groups. GAFA Geom. funct. anal. 18, 271–303 (2008). https://doi.org/10.1007/s00039-008-0657-8

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  • DOI: https://doi.org/10.1007/s00039-008-0657-8

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