Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Almost disjoint permutation groups


Author: Fred Galvin
Journal: Proc. Amer. Math. Soc. 124 (1996), 1723-1725
MSC (1991): Primary 20B07
DOI: https://doi.org/10.1090/S0002-9939-96-03264-9
MathSciNet review: 1317037
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A permutation group $G$ on a set $E$ of (infinite) cardinality $\kappa $ is almost disjoint if no element of $G$ except the identity has $\kappa $ fixed points, i.e., if $G$ is an almost disjoint family of subsets of $E\times E$. We show how almost disjoint permutation groups can be constructed from almost disjoint families of sets.


References [Enhancements On Off] (What's this?)

  • 1. James E. Baumgartner, Almost-disjoint sets, the dense set problem and the partition calculus, Ann. Math. Logic 9 (1976), no. 4, 401–439. MR 0401472, https://doi.org/10.1016/0003-4843(76)90018-8
  • 2. Fred Galvin, Generating countable sets of permutations, J. London Math. Soc. (2) 51 (1995), 230--242. CMP 95:10
  • 3. W. Sierpinski, Sur une décomposition d'ensembles, Monatsh. Math. Phys. 35 (1928), 239--242.
  • 4. Neil H. Williams, Combinatorial set theory, North-Holland, Amsterdam, 1977.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20B07

Retrieve articles in all journals with MSC (1991): 20B07


Additional Information

Fred Galvin
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-2142
Email: galvin@math.ukans.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03264-9
Received by editor(s): December 20, 1994
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1996 American Mathematical Society