Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Almost disjoint permutation groups

Author(s): 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:

1.: James E. Baumgartner, Almost-disjoint sets, the dense set problem and the partition calculus, Ann. Math. Logic 9 (1976), 401--439. MR 53:5299
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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