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The complexity of maximal cofinitary groups

Author: Bart Kastermans
Journal: Proc. Amer. Math. Soc. 137 (2009), 307-316
MSC (2000): Primary 03E47; Secondary 20Bxx
Published electronically: August 27, 2008
MathSciNet review: 2439455
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Abstract: A cofinitary group is a subgroup of the infinite symmetric group in which each element of the subgroup has at most finitely many fixed points. A maximal cofinitary group is a cofinitary group that is maximal with respect to inclusion. We investigate the possible complexities of maximal cofinitary groups. In particular we show that (1) under the axiom of constructibility there exists a coanalytic maximal cofinitary group and (2) there does not exist an eventually bounded maximal cofinitary group. We also suggest some further directions for investigation.

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Bart Kastermans
Affiliation: Department of Mathematics, University of Wisconsin, Madison, 480 Lincoln Drive, Madison, Wisconsin 53706

Received by editor(s): May 14, 2007
Received by editor(s) in revised form: January 30, 2008
Published electronically: August 27, 2008
Additional Notes: The author was partially supported by Sun Yat-Sen University, Guangzhou, China
Communicated by: Julia Knight
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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