Abstract

In previous work we showed that the only finite nonabelian simple group acting by diffeomorphisms on a homology 3-sphere is the alternating or dodecahedral group A₅. Here we characterize finite nonsolvable groups that act on a homology 3-sphere preserving orientation. We find exactly the finite nonsolvable groups that act orthogonally on the 3-sphere, plus two families of groups for which we do not know at present if they really can act on a homology 3-sphere.

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