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16.43 (2006)

Solved

Is there a partition of the group $\bigoplus_{\omega_1} (\mathbb{Z}/3\mathbb{Z})$ into three subsets whose complements do not contain cosets modulo infinite subgroups? (There is a partition into two such subsets.)

Contributor: E. G. Zelenyuk

Progress

Yes, moreover, every infinite abelian group with finitely many involutions can be partitioned into infinitely many subsets such that every coset modulo an infinite subgroup meets each subset of the partition (Y. Zelenyuk, J. Combin. Theory (A), 115 (2008), 331–339).

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