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arXiv · 1303.4612

Densities, submeasures and partitions of groups

Taras Banakh·Igor Protasov·Sergiy Slobodianiuk
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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.

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Taras Banakh, Igor Protasov, Sergiy Slobodianiuk. 2014-05-09. Densities, submeasures and partitions of groups. https://arxiv.org/abs/1303.4612

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