Combinatorica

, Volume 36, Issue 3, pp 365–369

Note: A conjecture on partitions of groups

Original Paper

DOI: 10.1007/s00493-014-3208-y

Cite this article as:
Protasov, I. & Slobodianiuk, S. Combinatorica (2016) 36: 365. doi:10.1007/s00493-014-3208-y

Abstract

We conjecture that every infinite group G can be partitioned into countably many cells \(G = \bigcup\limits_{n \in \omega } {A_n }\) such that cov(AnAn−1) = |G| for each nω Here cov(A) = min{|X|: X} ⊆ G, G = X A}. We confirm this conjecture for each group of regular cardinality and for some groups (in particular, Abelian) of an arbitrary cardinality.

Mathematics Subject Classification (2010)

03E05 20B07 20F69 

Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.KyivUkraine

Personalised recommendations