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Results tagged with finite-groups
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user 5069
Questions on group theory which concern finite groups.
3
votes
Accepted
Finite groups admitting free isometric actions on round spheres
After all these comments, a possible answer to your question goes as follows.
If $n$ is even, then the only group that can act freely and isometrically on $S^n$ is $\mathbb{Z}/2$. One way to see this …
- 1,415
2
votes
Actions of finite groups on exotic smooth manifolds of dimension >4
I think the answer is no. But I don't know the reason. I take the fact that exotic spheres in dimension 7 do not admit orientation reversing diffeomorphisms (but the standard sphere does) as a clue to …