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Protasov, Igor V.

Selective survey on subset combinatorics of groups. (English. Ukrainian original) Zbl 1283.20029

J. Math. Sci., New York 174, No. 4, 486-514 (2011); translation from Ukr. Mat. Visn. 7, No. 2, 220-257 (2010).
Summary: We survey recent results concerning the combinatorial size of subsets of groups. For a cardinal \(\kappa\), according to its arrangement in a group \(G\), a subset of \(G\) is distinguished as \(\kappa\)-large, \(\kappa\)-small, \(\kappa\)-thin, \(\kappa\)-thick, and \(P_\kappa\)-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.

Cited in 1 Review
Cited in 12 Documents

MSC:

20F05 Generators, relations, and presentations of groups
22A05 Structure of general topological groups
54H11 Topological groups (topological aspects)
05B40 Combinatorial aspects of packing and covering
43A07 Means on groups, semigroups, etc.; amenable groups

Keywords:

large subsets of groups; small subsets of groups; thin subsets of groups; thick subsets of groups; density; cellularity; resolvability; spread; packing numbers; kaleidoscopical configurations
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Full Text: DOI Link

References:

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