Geodesic
Finite groups of derangements on the \(n\)-Cube II
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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.
DOI : 10.37236/683
Classification : 05E18, 05E10, 52C99, 20B25 
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     author = {Larry Cusick and Oscar Vega},
     title = {Finite groups of derangements on the {\(n\)-Cube} {II}},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/683},
     zbl = {1235.05156},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/683/}
}
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Larry Cusick; Oscar Vega. Finite groups of derangements on the \(n\)-Cube II. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/683

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