Bulletin of Symbolic Logic

Isomorphism types of maximal cofinitary groups

Bart Kastermans

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Abstract

A cofinitary group is a subgroup of Sym(ℕ) where all nonidentity elements have finitely many fixed points. A maximal cofinitary group is a cofinitary group, maximal with respect to inclusion. We show that a maximal cofinitary group cannot have infinitely many orbits. We also show, using Martin's Axiom, that no further restrictions on the number of orbits can be obtained. We show that Martin's Axiom implies there exist locally finite maximal cofinitary groups. Finally we show that there exists a uniformly computable sequence of permutations generating a cofinitary group whose isomorphism type is not computable.

Article information

Source
Bull. Symbolic Logic, Volume 15, Issue 3 (2009), 300-319.

Dates
First available in Project Euclid: 1 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.bsl/1246453976

Digital Object Identifier
doi:10.2178/bsl/1246453976

Mathematical Reviews number (MathSciNet)
MR2604957

Zentralblatt MATH identifier
1183.03040

Citation

Kastermans, Bart. Isomorphism types of maximal cofinitary groups. Bull. Symbolic Logic 15 (2009), no. 3, 300--319. doi:10.2178/bsl/1246453976. https://projecteuclid.org/euclid.bsl/1246453976


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