Isomorphism types of maximal cofinitary groups
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.
Permanent link to this document: http://projecteuclid.org/euclid.bsl/1246453976
Digital Object Identifier: doi:10.2178/bsl/1246453976
Zentralblatt MATH identifier: 05608378
Mathematical Reviews number (MathSciNet): MR2604957