On Centres of 3-blocks of the Ree groups ${}^2{G}_2(q)$

Abstract

Let $G:={}^2{G}_2(q)$ be the simple Ree group with $q=3^{2k+1}$ and $k$ a positive integer. We show that the centre of the principal block $Z(kG{e}_0)$, where $k$ is an algebraically closed field of characteristic $3$, is not isomorphic to the centre of the Brauer corresponding block $Z(k{N}_G(P))$, where $N_G(P)$ is the normaliser in $G$ of a Sylow $3$-subgroup. As part of the proof, we compute the conjugacy classes of elements and the character tables of the maximal parabolic subgroups of $G$.

22 pages, Updated version

Cited by in corpus (1)

• Centres of blocks of finite groups with trivial intersection Sylow $p$-subgroups