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.
@article{bwmeta1.element.doi-10_1515_math-2017-0048,
author = {Roman Witu\l a and Edyta Hetmaniok and Damian S\l ota},
title = {Some new facts about group G generated by the family of convergent permutations},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {568-577},
zbl = {06715928},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0048}
}
Roman Wituła; Edyta Hetmaniok; Damian Słota. Some new facts about group 𝒢 generated by the family of convergent permutations. Open Mathematics, Tome 15 (2017) pp. 568-577. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0048/