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We introduce and investigate a class of profinite groups defined via extensions of centralizers analogous to the extensively studied class of finitely generated fully residually free groups, that is, limit groups (in the sense of Z. Sela). From the fact that the profinite completion of limit groups belong to this class, results on their group-theoretical structure and homological properties are obtained.
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Pavel A. Zalesskiĭ, Theo A.D. Zapata, Profinite extensions of centralizers and the profinite completion of limit groups. Rev. Mat. Iberoam. 36 (2020), no. 1, pp. 61–78DOI 10.4171/RMI/1121