The free rank of symmetry of (S n) k (Q1102586)
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scientific article; zbMATH DE number 4050569
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The free rank of symmetry of (S n) k |
scientific article; zbMATH DE number 4050569 |
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The free rank of symmetry of (S n) k (English)
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1988
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The main result of this paper is that if \(G=(Z/pZ)\) r, p an odd prime, acts freely on (S n) k, then \(r\leq k\). For \(p=2\), the result holds except possibly for \(n=1\), 3, or 7. For \(k=1\), this was proved by P. A. Smith, and the extension has long been sought. Recently, this was shown by G. Carlsson to be true for actions which were homologically trivial. This paper extends to more general actions by considering the representations that are possible.
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free actions of products of cyclic groups on products of spheres
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representations
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