Supplements of Bounded Groups
نویسنده
چکیده
Let be innnite cardinals and let be a set of cardinality. The bounded permutation group B ((), or simply B , is the group consisting of all permutations of which move fewer than points in. We say that a permutation group G acting on is a supplement of B if B G is the full symmetric group on. In 7], Macpherson and Neumann claimed to have classiied all supplements of bounded permutation groups. Speciically, they claimed to have proved that a group G acting on the set is a supplement of B if and only if there exists with jj < such that the setwise stabiliser G fg acts as the full symmetric group on n. However I have found a mistake in their proof. The aim of this paper is to examine conditions under which Macpherson and Neumann's claim holds, as well as conditions under which a counterexample can be constructed. In the process we will discover surprising links with cardinal arithmetic and Shelah's recently developed pcf theory.
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