Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4661188 | Topology and its Applications | 2006 | 10 Pages |
Abstract
The only finite non-Abelian simple group acting on a homology 3-sphere—necessarily non-freely—is the dodecahedral group A5≅PSL(2,5) (in analogy, the only finite perfect group acting freely on a homology 3-sphere is the binary dodecahedral group ). In the present paper we show that the only finite simple groups acting on a homology 4-sphere, and in particular on the 4-sphere, are the alternating or linear fractional groups A5≅PSL(2,5) and A6≅PSL(2,9). From this we deduce a short list of groups which contains all finite nonsolvable groups admitting an action on a homology 4-sphere.
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Mathematics
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