On a matrix group constructed from an {R,s+1,k}-potent matrix

Let R∈Cn×n be a {k}-involutory matrix (that is, Rk=In) for some integer k≥2, and let s be a nonnegative integer. A matrix A∈Cn×n is called an {R,s+1,k}-potent matrix if A satisfies RA=As+1R. In this paper, a matrix group corresponding to a fixed {R,s+1,k}-potent matrix is explicitly constructed, and properties of this group are derived and investigated. This group is then reconciled with the classical matrix group GA that is associated with a generalized group invertible matrix A.