Fernando Szechtman

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math.GR2026

A power-commutator presentation for the group of truncated polynomials under substitution

Fernando Szechtman

Given a prime $p$ , the Nottingham group $G (p)$ is the group of formal power series $x + a_{2} x^{2} + a_{3} x^{3} + \dots$ , $a_{i} \in Z / p Z$ , under substitution. For $n \geq 1$ , we write $…

math.GR2026

Substitution groups of formal power series

Agustín D'Alessandro, Fernando Szechtman

Let $G$ be the group of power series $x + a_{2} x^{2} + a_{3} x^{3} + \dots \in R [[x]]$ under substitution, where $R$ is a commutative ring with $1 \neq = 0$ of prime characteristic $p$ . Given any $n…

math.GR2026

A family of groups extending McLain's

Leandro Cagliero, Fernando Szechtman

Given a strict partial order $Δ$ on a set $Λ$ and an arbitrary ring $R$ with $1 \neq = 0$ , the corresponding McLain group $M (Δ)$ has been studied in depth. We construct a larger famil…

math.GR2024

The automorphism group of certain polycyclic groups

Khalid Benabdallah, Agustin D'Alessandro, Fernando Szechtman

For $β \in Z$ , let $G (β) = ⟨ A, B ∣ A^{[A, B]} = A, B^{[B, A]} = B^{β} ⟩$ be the infinite Macdonald group, and set $C = [A, B]$ . Then $G (β)$ is a nilpotent polycyclic gro…

math.GR2024

Sylow subgroups of the Macdonald group on 2 parameters

Fernando Szechtman

Consider the Macdonald group $G (α, β) = ⟨ A, B ∣ A^{[A, B]} = A^{α}, B^{[B, A]} = B^{β} ⟩$ , where $α$ and $β$ are integers different from one. We fill a gap in Macdonald's origin…

math.GR2024

A study of the Wamsley group and its Sylow subgroups

A. Previtali, F. Szechtman

We study the Wamsley group $⟨ X, Y, Z ∣ X^{Z} = X^{α},^{Z} Y = Y^{β}, Z^{γ} = [X, Y]⟩$ and its Sylow subgroups, where $α^{γ} \neq = 1 \neq = β^{γ}$ and $γ > 0$ , obtaining the sharpest results w…