N. Krylov

collaborators

4 papers

math.GR2025

Lower central series of the Riordan group over the field with two elements

Nikolai A. Krylov

The Riordan group $R$ over the field $F_{2}$ is a split extension of the Appell subgroup by the Nottingham group $N (F_{2})$ . Using the lower central s…

math.GR2025

The symmetric groups $S_{n}, n \geq 4$ , and finite non-abelian simple groups are not embeddable in any Riordan group

Tian-Xiao He, Nikolai A. Krylov

We prove that the symmetric group of degree greater than three cannot be embedded into the Riordan group with coefficients in any commutative ring. We also prove the impossibility…

math.CO2024

Periodic Column Partial Sums in the Riordan Array of a Polynomial

Nikolai A. Krylov

When $p (t)$ is a polynomial of degree $d$ , $k$ -th column of the Riordan array $(1/ (1 - t^{d + 1}), tp (t))$ is an eventually periodic sequence with the repeating part beginn…

math.GR2024

On embeddability of Coxeter groups into the Riordan group

Tian-Xiao He, Nikolai A. Krylov

We discuss examples of linear representations of finite groups as subgroups of the Riordan group. In particular, we show that the symmetric group of degree three has no faithful re…

Lower central series of the Riordan group over the field with two elements

The symmetric groups Sn​,n≥4, and finite non-abelian simple groups are not embeddable in any Riordan group

Periodic Column Partial Sums in the Riordan Array of a Polynomial

On embeddability of Coxeter groups into the Riordan group

The symmetric groups $S_{n}, n \geq 4$ , and finite non-abelian simple groups are not embeddable in any Riordan group