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Recent progress in subset combinatorics of groups

  • Igor V. Protasov
  • Ksenia D. Protasova
Article

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.

Keywords

Large, small, thin, thick, sparse, and scattered subsets of groups descriptive complexity Boolean algebra of subsets of a group Stone– Čech compactification ultracompanion Ramsey-product subset of a group recurrence combinatorial derivation 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Computer Science and CyberneticsTaras Shevchenko National University of KyivKyivUkraine

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