Abstract
We survey recent results concerning the combinatorial size of subsets of groups. For a cardinal κ, according to its arrangement in a group G, a subset of G is distinguished as κ-large, κ-small, κ-thin, κ-thick, and P κ -small. By analogy with topology, there arise the following combinatorial cardinal invariants of a group: density, cellularity, resolvability, spread, etc. The paper consists of 7 sections: Ballean context, Amenability, Ideals, Partitions, Packings, Around thin subsets, and Colorings.
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 7, No. 2, pp. 220–257, April–May, 2010.
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Protasov, I.V. Selective survey on Subset Combinatorics of Groups. J Math Sci 174, 486–514 (2011). https://doi.org/10.1007/s10958-011-0314-x
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DOI: https://doi.org/10.1007/s10958-011-0314-x