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 
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), no. 4, 401–439. MR 401472, 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.
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
