Normal elements of completed group algebras over ${\mathrm{SL}}_3({\mathbb{Z}}_p)$

Abstract

Let $p$ be a prime integer and ${\mathbb{Z}}_p$ be the ring of $p$-adic integers. By a purely computational approach we prove that each nonzero normal element of a completed group algebra over the special linear group ${\mathrm{SL}}_3({\mathbb{Z}}_p)$ is a unit. This give a positive answer to an open question in \cite{WeiBian2} and make up for an earlier mistake in \cite{WeiBian1} simultaneously.

References in corpus (2)

• Presentation of the Iwasawa algebra of the first congruence kernel of a semi-simple, simply connected Chevalley group over ${\mathbb{Z}}_p$
• Presentation of the Iwasawa algebra of the pro-$p$ Iwahori subgroup of $G{L}_n({\mathbb{Z}}_p)$

Cited by in corpus (1)

• Presentation of the Iwasawa algebra of the pro-$p$ Iwahori subgroup of $G{L}_n({\mathbb{Z}}_p)$