Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2007 | 196 | 3 | 197-235
Tytuł artykułu

Possible cardinalities of maximal abelian subgroups of quotients of permutation groups of the integers

Treść / Zawartość
Warianty tytułu
Języki publikacji
If G is a group then the abelian subgroup spectrum of G is defined to be the set of all κ such that there is a maximal abelian subgroup of G of size κ. The cardinal invariant A(G) is defined to be the least uncountable cardinal in the abelian subgroup spectrum of G. The value of A(G) is examined for various groups G which are quotients of certain permutation groups on the integers. An important special case, to which much of the paper is devoted, is the quotient of the full symmetric group by the normal subgroup of permutations with finite support. It is shown that, if we use G to denote this group, then A(G) ≤ 𝔞. Moreover, it is consistent that A(G) ≠ 𝔞. Related results are obtained for other quotients using Borel ideals.
Słowa kluczowe
  • Department of Mathematics, Rutgers University, Hill Center, Piscataway, NJ 08854-8019, U.S.A.
  • Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, Israel
  • Department of Mathematics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3
  • Fields Institute, 222 College Street, Toronto, Canada M5T 3J1
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.