Commutators and commutator subgroups of the Riordan group (Q6110352)

The Riordan group was introduced, under this name and in a more restrictive context, by \textit{L. Shapiro} et al. in [Discrete Appl. Math. 34, No. 1--3, 229--239 (1991; Zbl 0754.05010)]. Let \(R\) be the Riordan group over a field \(\mathbb{K}\). In the paper under review, the authors exhaustively describe the terms \(R^{(n)}\) of the derived series of \(R\) (see Theorem 1). A nice consequence is that all elements of \(R^{(n)}\) are commutators of elements of \(R^{(n-1)}\).