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Preprint Number 485

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485. Oleg Belegradek
Homogeneity in relatively free groups

Submission date: 31 July 2012.


We prove that any torsion-free, residually finite relatively free group of infinite rank is not \aleph_1-homogeneous. This generalizes R. Sklinos' result that a free group of infinite rank is not \aleph_1-homogeneous, and, in particular, gives a new simple proof of that result.

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