Maximal subgroup of semigroup of generalized circulant Boolean matrices (Q1123983)

The set of all r-circulant Boolean matrices for \(r=0,1,...,n-1\) forms a semigroup, called the semigroup of generalized circulant Boolean matrices and denoted by \(G_ n\), under matrix multiplication and by Boolean operations for the entries of matrices. In this letter we characterize the maximal subgroup, denoted by M(E), of the semigroup \(G_ n\) containing an idempotent r-circulant Boolean matrix E.