English

Recent progress in subset combinatorics of groups

Combinatorics 2018-02-13 v1 Group Theory

Abstract

We systematize and analyze some results obtained in Subset Combinatorics of GG groups after publications the previous surveys [1-4]. The main topics: the dynamical and descriptive characterizations of subsets of a group relatively their combinatorial size, Ramsey-product subsets in connection with some general concept of recurrence in GG-spaces, new ideals in the Boolean algebra PG\mathcal{P}_{G} of all subsets of a group GG and in the Stone-Cˇ\check{C}ech compactification βG\beta G of GG , the combinatorial derivation.

Keywords

Cite

@article{arxiv.1802.04106,
  title  = {Recent progress in subset combinatorics of groups},
  author = {Igor Protasov and Ksenia Protasova},
  journal= {arXiv preprint arXiv:1802.04106},
  year   = {2018}
}

Comments

Large, small, thin, thick, sparse and scattered subsets of groups; descriptive complexity; Boolean algebra of subsets of a group; Stone-$\check{C}$ech compactification; ultracompanion; Ramsey-product subset of a group; recurrence; combinatorial derivation. arXiv admin note: text overlap with arXiv:1704.02494

R2 v1 2026-06-23T00:19:22.768Z