PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Colloquium Mathematicum

2008 | 112 | 1 | 163-173
Tytuł artykułu

### Highly transitive subgroups of the symmetric group on the natural numbers

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
163-173
Opis fizyczny
Daty
wydano
2008
Twórcy
autor
• Mathematics Department, University of Louisville, Louisville, KY 40292, U.S.A.
autor
• Mathematics Institute, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, UK
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory