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Tkachenko showed in 1990 the existence of a countably compact group topology on the free Abelian group of size c using CH. Koszmider, Tomita and Watson showed in 2000 the existence of a countably compact group topology on the free Abelian group of size 2 c using a forcing model in which CH holds. Wallace's question from 1955, asks whether every both-sided cancellative countably compact semigroup is a topological group. A counterexample to Wallace's question has been called a Wallace semigroup.doi:10.1016/j.topol.2006.03.028 fatcat:ueqte3swjfcdxge5asrdlugtpy