ScholarLens Back to search
2020•arXiv (Cornell University)Open access

Diameter of Cayley graphs of $SL(n,p)$ with generating sets containing a\n transvection

Zoltán Halasi

Open full text 0 citations

Abstract

A well-known conjecture of Babai states that if $G$ is a finite simple group\nand $X$ is a generating set of $G$, then the diameter of the Cayley graph\n$Cay(G,X)$ is bounded above by $(\\log |G|)^c$ for some absolute constant $c$.\nThe goal of this paper is to prove such a bound for the diameter of $Cay(G,X)$\nwhenever $G=SL(n,p)$ and $X$ is a generating set of $G$ which contains a\ntransvection. A natural analogue of this result is also proved for $G=SL(n,K)$,\nwhere $K$ can be any field.\n

Open-access reader

About this research paper

What this paper is about

A well-known conjecture of Babai states that if $G$ is a finite simple group\nand $X$ is a generating set of $G$, then the diameter of the Cayley graph\n$Cay(G,X)$ is bounded above by $(\\log |G|)^c$ for some absolute constant $c$.\nThe goal of this paper is to prove such a bound for the diameter of $Cay(G,X)$\nwhenever $G=SL(n,p)$ and $X$ is a generating set of $G$ which contains a\ntransvection. A natural analogue of this result is also proved for $G=SL(n,K)$,\nwhere $K$ can be any field.\n

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

A well-known conjecture of Babai states that if $G$ is a finite simple group\nand $X$ is a generating set of $G$, then the diameter of the Cayley graph\n$Cay(G,X)$ is bounded above by $(\\log |G|)^c$ for some absolute constant $c$.\nThe goal of this paper is to prove such a bound for the diameter of $Cay(G,X)$\nwhenever $G=SL(n,p)$ and $X$ is a generating set of $G$ which contains a\ntransvection. A natural analogue of this result is also proved for $G=SL(n,K)$,\nwhere $K$ can be any field.\n

Key concepts: Cayley graph, Generating set of a group, Combinatorics, Mathematics, Conjecture, Bounded function, Graph, Cayley's theorem

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Diameter of Cayley graphs of $SL(n,p)$ with generating sets containing a\n transvection — Research Paper | ScholarLens