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Displaying similar documents to “The existence of initially ω 1 -compact group topologies on free Abelian groups is independent of ZFC”

A group topology on the free abelian group of cardinality 𝔠 that makes its square countably compact

Ana Carolina Boero, Artur Hideyuki Tomita (2011)

Fundamenta Mathematicae

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Under 𝔭 = 𝔠, we prove that it is possible to endow the free abelian group of cardinality 𝔠 with a group topology that makes its square countably compact. This answers a question posed by Madariaga-Garcia and Tomita and by Tkachenko. We also prove that there exists a Wallace semigroup (i.e., a countably compact both-sided cancellative topological semigroup which is not a topological group) whose square is countably compact. This answers a question posed by Grant.

Subsequence sums of zero-sum free sequences over finite abelian groups

Yongke Qu, Xingwu Xia, Lin Xue, Qinghai Zhong (2015)

Colloquium Mathematicae

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Let G be a finite abelian group of rank r and let X be a zero-sum free sequence over G whose support supp(X) generates G. In 2009, Pixton proved that | Σ ( X ) | ≥ 2 r - 1 ( | X | - r + 2 ) - 1 for r ≤ 3. We show that this result also holds for abelian groups G of rank 4 if the smallest prime p dividing |G| satisfies p ≥ 13.