Some inverse limit approaches to the Riordan group

Commutators and commutator subgroups of the Riordan group

“…For every n ∈ N consider the general linear group GL(n + 1, K) formed by all (n + 1) × (n + 1) invertible matrices with coefficients in K. Since every Riordan matrix is lower triangular we have a natural homomorphism Π n : R → GL(n + 1, K) given by Π n (( [23]. We denote by (d, h) n = Π n ((d, h)) and by R n = Π n (R).…”

“…Using the inverse limit approach to the Riordan group (see again [23]), this is equivalent to showing that there exists a unique sequence of finite Riordan matrices (B 0 , B 1 , B 2 , . .…”

“…During the last few years, the Riordan group and some related topics have been studied in [3, 6-8, 13, 18, 25, 26, 31, 41]. For the purpose of this paper, it is of special interest the work [23], where the Riordan group is described as an inverse limit of an inverse sequence of groups of finite matrices.…”

“…The derived series is also an important aspect to understand the algebraic structure of the Riordan group. Moreover, analogous description of commutators subgroups for the Riordan groups of finite matrices introduced in [23] is also provided as a consequence of Theorem 1. These groups of finite matrices turn out to be solvable and, consequently, the Riordan group is a pro-solvable group.…”

Algebraic and topological properties of Riordan groups over finite fields

“…To be not exhausted, we only list a few of works related to Riordan groups [7, 14, 21-24, 28, 29] and references there in. Recently, in 2017 via the inverse limit approaches of Riordan group initiated in [20], the authors established an infinitedimesnional Fréchet Lie group and the corresponding Lie algebra on the Riordan group [8].…”