In the paper we present the selected properties of composition re-lation of the convergent and divergent permutations connected withcommutation. We note that a permutation on $ \matbb{N} $i s called the conver-gent permutation if for each convergent series$\Sigma a_n$of real terms the$p$−rearranged series $\Sigma a_p(n)$ is also convergent.All the other permu-tations on $ \matbb{N} $ are called the divergent permutations. We have proven,among others, that for many permutations p on $ \matbb{N} $ the family of diver-gent permutations $q$ on $ \matbb{N} $, commuting with $p$, possesses cardinality ofthe continuum. For example, the permutations $p$ on $ \matbb{N} $ having finiteorder possess this property. For contrast, the example of convergentpermutation which commute only with some convergent permutationsis also presented.
@article{259,
title = {On commutation properties of the composition relation of convergent and divergent permutations PART I},
journal = {Tatra Mountains Mathematical Publications},
volume = {58},
year = {2014},
doi = {10.2478/tatra.v58i0.259},
language = {EN},
url = {http://dml.mathdoc.fr/item/259}
}
Wituła, Roman; Hetmaniok, Edyta; Słota, Damian. On commutation properties of the composition relation of convergent and divergent permutations PART I. Tatra Mountains Mathematical Publications, Tome 58 (2014) . doi : 10.2478/tatra.v58i0.259. http://gdmltest.u-ga.fr/item/259/