Highly transitive subgroups of the symmetric group on the natural numbers

U. B. Darji, and J. D. Mitchell. "Highly transitive subgroups of the symmetric group on the natural numbers." Colloquium Mathematicae 112.1 (2008): 163-173. <http://eudml.org/doc/284300>.

@article{U2008,
abstract = {Highly transitive subgroups of the symmetric group on the natural numbers are studied using combinatorics and the Baire category method. In particular, elementary combinatorial arguments are used to prove that given any nonidentity permutation α on ℕ there is another permutation β on ℕ such that the subgroup generated by α and β is highly transitive. The Baire category method is used to prove that for certain types of permutation α there are many such possibilities for β. As a simple corollary, if $2 ≤ κ ≤ 2^\{ℵ₀\}$, then the free group of rank κ has a highly transitive faithful representation as permutations on the natural numbers.},
author = {U. B. Darji, J. D. Mitchell},
journal = {Colloquium Mathematicae},
keywords = {highly transitive permutation groups; symmetric group on countable set},
language = {eng},
number = {1},
pages = {163-173},
title = {Highly transitive subgroups of the symmetric group on the natural numbers},
url = {http://eudml.org/doc/284300},
volume = {112},
year = {2008},
}

TY - JOUR
AU - U. B. Darji
AU - J. D. Mitchell
TI - Highly transitive subgroups of the symmetric group on the natural numbers
JO - Colloquium Mathematicae
PY - 2008
VL - 112
IS - 1
SP - 163
EP - 173
AB - Highly transitive subgroups of the symmetric group on the natural numbers are studied using combinatorics and the Baire category method. In particular, elementary combinatorial arguments are used to prove that given any nonidentity permutation α on ℕ there is another permutation β on ℕ such that the subgroup generated by α and β is highly transitive. The Baire category method is used to prove that for certain types of permutation α there are many such possibilities for β. As a simple corollary, if $2 ≤ κ ≤ 2^{ℵ₀}$, then the free group of rank κ has a highly transitive faithful representation as permutations on the natural numbers.
LA - eng
KW - highly transitive permutation groups; symmetric group on countable set
UR - http://eudml.org/doc/284300
ER -