On finite simple and nonsolvable groups acting on homology 4-spheres
نویسنده
چکیده
The only finite nonabelian 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 A∗5 ∼= SL(2, 5)). 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 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-spheres. 1991 Mathematics Subject Classification. 57M60, 57S17, 57S25
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تاریخ انتشار 2005