Finite Groups of Derangements on the $n$-Cube II
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, $\gcd(k, |G|)=2^s$ for some non-negative integer $s$. The proof of this result is existential but does give some ideas on what $n$ could be.
2009 ◽
Vol 79
(1)
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pp. 23-30
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1969 ◽
Vol 10
(3-4)
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pp. 359-362
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2021 ◽
Vol 58
(2)
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pp. 147-156
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1997 ◽
Vol 40
(2)
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pp. 243-246
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2008 ◽
Vol 07
(06)
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pp. 735-748
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1986 ◽
Vol 40
(2)
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pp. 253-260
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