Displaying similar documents to “Three Notes on Permutations.”

Axial permutations of ω²

Paweł Klinga (2016)

Colloquium Mathematicae

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We prove that every permutation of ω² is a composition of a finite number of axial permutations, where each axial permutation moves only a finite number of elements on each axis.

Some new facts about group 𝒢 generated by the family of convergent permutations

Roman Wituła, Edyta Hetmaniok, Damian Słota (2017)

Open Mathematics

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The aim of this paper is to present some new and essential facts about group 𝒢 generated by the family of convergent permutations, i.e. the permutations on ℕ preserving the convergence of series of real terms. We prove that there exist permutations preserving the sum of series which do not belong to 𝒢. Additionally, we show that there exists a family G (possessing the cardinality equal to continuum) of groups of permutations on ℕ such that each one of these groups is different than...