The existence of initially $\omega _1$-compact group topologies on free Abelian groups is independent of ZFC

Artur Hideyuki Tomita

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.

On subsequence sums of a zero-sum free sequence.

Sun, Fang (2007)

The Electronic Journal of Combinatorics [electronic only]

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Term functions on non-Abelian groups of order $p q$

Hans Lausch (1982)

Archivum Mathematicum

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A note on free abelian groups

Ladislav Procházka (1969)

Commentationes Mathematicae Universitatis Carolinae

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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 $| Σ (X) | \geq 2^{r - 1} (| X | - r + 2) - 1$ 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.

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

On subsequence sums of a zero-sum free sequence.

Term functions on non-Abelian groups of order p q

A note on free abelian groups

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

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

Term functions on non-Abelian groups of order $p q$