Back to Search
Start Over
Normalisers of maximal tori and a conjecture of Vdovin
- Publication Year :
- 2022
-
Abstract
- Let $G = O^{p'}(\bar{G}^F)$ be a finite simple group of Lie type defined over a field of characteristic $p$, where $F$ is a Steinberg endomorphism of the ambient simple algebraic group $\bar{G}$. Let $\bar{T}$ be an $F$-stable maximal torus of $\bar{G}$ and set $N = N_G(\bar{T})$. A conjecture due to Vdovin asserts that if $G \not\cong {\rm L}_3(2)$ then $N \cap N^x$ is a $p$-group for some $x \in G$. In this paper, we use a combination of probabilistic and computational methods to calculate the base size for the natural action of $G$ on $G/N$, which allows us to prove a stronger, and suitably modified, version of Vdovin's conjecture.<br />Comment: 33 pages; to appear in J Algebra
- Subjects :
- Mathematics - Group Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2207.09495
- Document Type :
- Working Paper