The canonical completion of Haglund and Wise ("Special Cube Complexes", GAFA, 2008, see Section 6) is a great strengthening of Stallings Theorem (I wrote a quantified version of this in a paper, available on the arXiv, with Mark Hagen and Priyam Patel called "Residual finiteness growth of virtually special groups").
Khalid Bou-Rabee
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