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Proceedings of the American Mathematical Society

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Almost disjoint permutation groups

Author: Fred Galvin
Journal: Proc. Amer. Math. Soc. 124 (1996), 1723-1725
MSC (1991): Primary 20B07
MathSciNet review: 1317037
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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 401472,
  • 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.

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Additional Information

Fred Galvin
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-2142

Received by editor(s): December 20, 1994
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1996 American Mathematical Society