Finite groups of derangements on the \(n\)-Cube II (Q640459)
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scientific article; zbMATH DE number 5960058
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite groups of derangements on the \(n\)-Cube II |
scientific article; zbMATH DE number 5960058 |
Statements
Finite groups of derangements on the \(n\)-Cube II (English)
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18 October 2011
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Summary: Given \(k \in \mathbb{N}\) and a finite group \(G\), it is shown that \(G\) is isomorphic to a subgroup of the group of symmetries of some \(n\)-cube in such a way that \(G\) acts freely on the set of \(k\)-faces, if and only if, \(\text{gcd}(k, |G|) = 2^s\) for some non-negative integer \(s\). The proof of this result is existential but does give some ideas on what \(n\) could be.
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