Counting coarse subsets of a countable group

Igor Protasov, Ksenia Protasova

Abstract

For every countable group G, there are 2ω distinct classes of coarselyequivalent subsets of G.


Keywords

ballean; coarse structure; asymorphism; coarse equivalence

Subject classification

54E15; 20F69.

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References

T. Banakh, J. Higes and M. Zarichnyi, The coarse classification of countable abelian groups, Trans. Amer. Math. Soc. 362 (2010), 4755-4780. https://doi.org/10.1090/S0002-9947-10-05118-4

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P. de la Harpe, Topics in geometric group theory, University Chicago Press, 2000.

I. V. Protasov, Morphisms of ball structures of groups and graphs, Ukr. Mat. Zh. 53 (2002), 847-855.

I. Protasov and T. Banakh, Ball structures and colorings of groups and graphs, Math. Stud. Monogr. Ser., Vol. 11, VNTL, Lviv, 2003.

I. Protasov and M. Zarichnyi, General asymptology, Math. Stud. Monogr. Ser., Vol. 12, VNTL, Lviv, 2007.

J. Roe, Lectures on coarse geometry, Amer. Math. Soc., Providence, R.I, 2003.

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Universitat Politècnica de València

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