On the catenarity of virtually nilpotent mod-$p$ Iwasawa algebras

TL;DR

This paper proves that the completed group ring of a nilpotent-by-finite compact p-adic analytic group over a finite field of characteristic p is a catenary ring, contributing to the understanding of its algebraic structure.

Contribution

It establishes the catenarity of the completed group ring for a broad class of p-adic analytic groups, a result not previously known.

Findings

kG is a catenary ring for the specified groups

Provides structural insights into completed group rings over finite fields

Advances the theory of p-adic analytic group algebras

Abstract

Let $p>2$ be a prime, $k$ a finite field of characteristic $p$, and $G$ a nilpotent-by-finite compact $p$-adic analytic group. Write $kG$ for the completed group ring of $G$ over $k$. We show that $kG$ is a catenary ring.