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

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Abstract | References | Similar Articles | Additional Information

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

**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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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