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

Roman Wituła; Edyta Hetmaniok; Damian Słota

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 568-577
- ISSN: 2391-5455

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topRoman Wituła, Edyta Hetmaniok, and Damian Słota. "Some new facts about group 𝒢 generated by the family of convergent permutations." Open Mathematics 15.1 (2017): 568-577. <http://eudml.org/doc/288149>.

@article{RomanWituła2017,

abstract = {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 𝒢 and is composed only from the permutations preserving the sum of series. This result substantially strengthens some old Pleasants’ result.},

author = {Roman Wituła, Edyta Hetmaniok, Damian Słota},

journal = {Open Mathematics},

keywords = {Convergent permutations; Divergent permutations; b-connected permutations; convergent permutations; divergent permutations; $b$-connected permutations},

language = {eng},

number = {1},

pages = {568-577},

title = {Some new facts about group 𝒢 generated by the family of convergent permutations},

url = {http://eudml.org/doc/288149},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Roman Wituła

AU - Edyta Hetmaniok

AU - Damian Słota

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

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 568

EP - 577

AB - 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 𝒢 and is composed only from the permutations preserving the sum of series. This result substantially strengthens some old Pleasants’ result.

LA - eng

KW - Convergent permutations; Divergent permutations; b-connected permutations; convergent permutations; divergent permutations; $b$-connected permutations

UR - http://eudml.org/doc/288149

ER -

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