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MR1332302 (96d:20020) 20E05 (03C60 20F10)
Remeslennikov, V. N. $\exists$-free groups and groups with length function. Second International Conference on Algebra (Barnaul, 1991), 369--376, Contemp. Math., 184, Amer. Math. Soc., Providence, RI, 1995.
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