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Homogeneity in relatively free groups

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We prove that any torsion-free, residually finite relatively free group of infinite rank is not \({\aleph_1}\) -homogeneous. This generalizes 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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Correspondence to Oleg Belegradek.

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Belegradek, O. Homogeneity in relatively free groups. Arch. Math. Logic 51, 781–787 (2012). https://doi.org/10.1007/s00153-012-0298-3

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  • Group variety
  • Relatively free group
  • Homogeneous structure

Mathematics Subject Classification (2000)

  • 20E10
  • 03C50