%0 Journal Article
%T A conjecture on partitions of groups
%A Igor Protasov
%A Sergii Slobodianiuk
%J Mathematics
%D 2014
%I arXiv
%X We conjecture that every infinite group $G$ can be partitioned into countably many cells $G=\bigcup_{n\in\omega}A_n$ such that $cov(A_nA_n^{-1})=|G|$ for each $n\in\omega$. Here $cov(A)=\min\{|X|:X\subseteq G, G=XA\}$. We confirm this conjecture for each group of regular cardinality and for some groups (in particular, Abelian) of an arbitrary cardinality.
%U http://arxiv.org/abs/1408.6259v1