We prove that if a finite group G acts smoothly on a manifold M so that all the isotropy subgroups are abelian groups with rank ≤ k, then G acts freely and smoothly on M ×S1 × · · ·×Sk for some positive integers n1, . . . , nk. We construct these actions using a recursive method, introduced in an earlier paper, that involves abstract fusion systems on… (More)

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