Normality in group rings

Let $KG$ be the group ring of a group $G$ over a commutative ring $K$ with unity. The rings $KG$ are described for which $xx^\sigma=x^\sigma x$ for all $x=\sum_{g\in G}\alpha_gg\in KG$, where \quad $x\mapsto x^\sigma=~\sum_{g\in G}\alpha_gf(g)\sigma(g)$\quad is an involution of $KG$; here $f: G\to U(K)$ is a homomorphism and $\sigma$ is an anti-automorphism of order two of $G$.Comment: 8 page

Torsion Units for a Ree group, Tits group and a Steinberg triality group

We investigate the Zassenhaus conjecture for the Steinberg triality group ${}^3D_4(2^3)$, Tits group ${}^2F_4(2)'$ and the Ree group ${}^2F_4(2)$. Consequently, we prove that the Prime Graph question is true for all three groups