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Recent progress in subset combinatorics of groups

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Abstract

We systematize and analyze some results obtained in the subset combinatorics of G groups presented in previous surveys [1,2,3,4]. The main topics: the dynamical and descriptive characterizations of subsets of a group relatively to their combinatorial size, Ramsey-product subsets in connection with some general concept of recurrence in G-spaces, new ideals in the Boolean algebra \( {\mathcal{P}}_G \) of all subsets of a group G and in the Stone– Čech compactification βG of G, and the combinatorial derivation.

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Authors and Affiliations

  1. Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Igor V. Protasov & Ksenia D. Protasova

Authors
  1. Igor V. Protasov
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  2. Ksenia D. Protasova
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Correspondence to Igor V. Protasov.

Additional information

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 14, No. 4, pp. 532–547 October–December, 2017.

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Protasov, I.V., Protasova, K.D. Recent progress in subset combinatorics of groups. J Math Sci 234, 49–60 (2018). https://doi.org/10.1007/s10958-018-3980-0

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  • DOI: https://doi.org/10.1007/s10958-018-3980-0

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