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September 2009 Isomorphism types of maximal cofinitary groups
Bart Kastermans
Bull. Symbolic Logic 15(3): 300-319 (September 2009). DOI: 10.2178/bsl/1246453976

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.

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Bart Kastermans. "Isomorphism types of maximal cofinitary groups." Bull. Symbolic Logic 15 (3) 300 - 319, September 2009. https://doi.org/10.2178/bsl/1246453976

Information

Published: September 2009
First available in Project Euclid: 1 July 2009

zbMATH: 1183.03040
MathSciNet: MR2604957
Digital Object Identifier: 10.2178/bsl/1246453976

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.15 • No. 3 • September 2009
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