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Constructing a maximal cofinitary group. (English) Zbl 1028.20001
A subgroup \(G\) of the symmetric group \(\text{Sym}(\omega)\) is ‘cofinitary’ if every non-identity element of \(G\) has just finitely many fixed points. See [P. J. Cameron, Bull. Lond. Math. Soc. 28, No. 2, 113-140 (1996; Zbl 0853.20002)] for a survey of cofinitary groups. By Zorn’s Lemma, every cofinitary group is contained in a ‘maximal cofinitary group’, that is, one maximal among the cofinitary subgroups of \(\text{Sym}(\omega)\). Assuming CH, the author gives a rather more concrete step-by-step construction of a maximal cofinitary group. He gives an analogous construction under Martin’s Axiom and the negation of CH.

20B07 General theory for infinite permutation groups
20E28 Maximal subgroups
20B35 Subgroups of symmetric groups
03E50 Continuum hypothesis and Martin’s axiom
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