  For a prime $p>2$, let $G$ be a semi-simple, simply connected, split
Chevalley group over $\mathbb{Z}_p$, $G(1)$ be the first congruence kernel of
$G$ and $\Omega_{G(1)}$ be the mod-$p$ Iwasawa algebra defined over the finite
field $\mathbb{F}_p$. Ardakov, Wei, Zhang have shown that if $p$ is a "nice
prime " ($p \geq 5$ and $p \nmid n+1$ if the Lie algebra of $G(1)$ is of type
$A_n$), then every non-zero normal element in $\Omega_{G(1)}$ is a unit.
Furthermore, they conjecture in their paper that their nice prime condition is
superfluous. The main goal of this article is to provide an entirely new proof
of Ardakov, Wei and Zhang's result using explicit presentation of Iwasawa
algebra developed by the second author of this article and thus eliminating the
nice prime condition, therefore proving their conjecture.
