Densities, submeasures and partitions of groups

Taras Banakh; Igor Protasov; Sergiy Slobodianiuk

Densities, submeasures and partitions of groups

Group Theory 2014-12-04 v4 Combinatorics

Authors: Taras Banakh , Igor Protasov , Sergiy Slobodianiuk

Abstract

In 1995 in Kourovka notebook the second author asked the following problem: it is true that for each partition $G=A_1\cup\dots\cup A_n$ of a group $G$ there is a cell $A_i$ of the partition such that $G=FA_iA_i^{-1}$ for some set $F\subset G$ of cardinality $|F|\le n$ ? In this paper we survey several partial solutions of this problem, in particular those involving certain canonical invariant densities and submeasures on groups.

Keywords

group partitions invariant densities submeasures Kourovka notebook finite covering group theory combinatorial group theory

Cite

@article{arxiv.1303.4612,
  title  = {Densities, submeasures and partitions of groups},
  author = {Taras Banakh and Igor Protasov and Sergiy Slobodianiuk},
  journal= {arXiv preprint arXiv:1303.4612},
  year   = {2014}
}

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14 pages (this is an update of the preceding version)

Densities, submeasures and partitions of groups

Abstract

Keywords

Cite

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