, Volume 36, Issue 3, pp 365–369 | Cite as

Note: A conjecture on partitions of groups

  • Igor Protasov
  • Sergii Slobodianiuk
Original Paper


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(A n A n −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 


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Copyright information

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

Authors and Affiliations

  1. 1.KyivUkraine

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