Finite Groups of Derangements on the \(n\)-Cube

Abstract

W. Y. C. Chen and R. P. Stanley have characterized the symmetries of the \(n\)-cube that act as derangements on the set of \(k\)-faces. In this paper we aim to use their result to characterize those finite subgroups of symmetries whose non-trivial members are derangements of the set of \(k\)-faces.