Highly transitive subgroups of the symmetric group on the natural numbers

• Autorzy: U. B. Darji , J. D. Mitchell
• 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.

Kategorie tematyczne

• 54H11: Topological groups
• 20B35: Subgroups of symmetric groups
• 20B22: Multiply transitive infinite groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 112
• Numer: 1
• Strony: 163-173

Daty

wydano

2008

Twórcy

autor

U. B. Darji

• Mathematics Department, University of Louisville, Louisville, KY 40292, U.S.A.

autor

J. D. Mitchell

• Mathematics Institute, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, UK

Identyfikatory

DOI

10.4064/cm112-1-9