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Alexander Skutin

Publications and source records attributed to Alexander Skutin.

8 recordsLinked to original sources
arXiv2026

On the class-breadth conjecture for $p>2$ -groups

The class-breadth conjecture of Leedham-Green, Neumann and Wiegold states that the nilpotency class of any $p$-group is at most $b(G) + 1$, where $\displaystyle{b(G) = \max_{g\in G}\log_p[G:Z_G(g)]}$ denotes the breadth of $G$. While several counter-examples to this conjecture have been found for $p = 2$, it is still open in general for $p>2$. This article is dedicated to the general case $p>2$ of the conjecture. We propose a generalization for the case $p>2$, which we prove under some additional conditions.

math.GR↗
arXiv2025

On the class-breadth conjecture

The class-breadth conjecture of Leedham-Green, Neumann and Wiegold states that for each $p$-group, $cl(G)\leq b(G) + 1$, where $cl(G)$, $b(G)$ denote the nilpotency class and the breadth of $G$. While several counter-examples to this conjecture have been found for $p = 2$, it is still open in general for $p > 2$. This article is dedicated to the general case $p > 2$ of the conjecture.

math.GR↗
arXiv2021

Cosmology of Plane Geometry

This paper focuses on a new approach to plane geometry and develops important concepts that can allow researchers to unite and observe plane geometry from a new, meaningful perspective.

math.MG↗
arXiv2020

Maximal Lie subalgebras of locally nilpotent derivations

It has been conjectured by Gene Freudenburg that for a polynomial ring, the triangular Lie algebra is the maximal Lie algebra which lies in the set of locally nilpotent derivations of the ring. Also it was conjectured that each other maximal Lie algebra which lies in the set of locally nilpotent derivations of the polynomial ring is conjugated to the triangular Lie algebra. In the present work we prove the first part of this conjecture and provide the counterexample to the second part. Also we show that the second part of the conjecture holds for the maximal Lie algebras among locally nilpotent derivations with some natural additional properties.

math.AC↗
arXiv2018

Proof of a Conjecture of Wiegold

In this short note we confirm a conjecture of James Wiegold. We prove that if $G$ is a finite $p$-group and $|G'|>p^{n(n-1)/2}$ for some non-negative integer $n$, then the group $G$ can be generated by the elements of breadth at least $n$. The breadth $b(x)$ of an element $x$ of a finite $p$-group $G$ is defined by the equation $|G:C_G(x)| = p^{b(x)}$, where $C_G(x)$ is the centralizer of $x$ in $G$.

math.GR↗