Commutators and commutator subgroups of the Riordan group

2021/08/01 by Luzón, Ana, Morón, Manuel A., Prieto-Martínez, Luis Felipe · 3 citations
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2108.00486

Abstract

We calculate the derived series of the Riordan group. To do that, we study a nested sequence of its subgroups, herein denoted by \mathcal G_k. By means of this sequence, we first obtain the n-th commutator subgroup of the Associated subgroup. This fact allows us to get some related results about certain groups of formal power series and to complete the proof of our main goal, Theorem 1 in this paper.

Cited by

• Lower central series of the Riordan group over the field with two elements
• Roots in the substitution group and in the group of Riordan matrices with ones in the main diagonal
• The symmetric groups S_n, n≥ 4, and finite non-abelian simple groups are not embeddable in any Riordan group

Related

• The group generated by Riordan involutions
• Riordan Groups in higher Dimensions
• On Generalized Commutator
• Elements of Finite Order in the Riordan Group and Their Eigenvectors
• Roots in the substitution group and in the group of Riordan matrices with ones in the main diagonal