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On the Coherency of Completed Group Algebra

David Burns, Yu Kuang, Dingli Liang

Abstract

We investigate coherency properties of certain completed integral group rings, precisely for compact $p$-adic Lie groups.

On the Coherency of Completed Group Algebra

Abstract

We investigate coherency properties of certain completed integral group rings, precisely for compact -adic Lie groups.
Paper Structure (8 sections, 9 theorems, 47 equations)

This paper contains 8 sections, 9 theorems, 47 equations.

Table of Contents

  1. Introduction
  2. Coherence results
  3. The proof of Theorem \ref{['general result']}
  4. Examples
  5. $n$-coherence results
  6. Nakayama's Lemma
  7. Ddivisibility of Tor-groups
  8. The proof of Theorem \ref{['strong coherent thm']}

Key Result

Theorem 1.1

If $G$ has a countable basis of neighbourhoods of the identity and a non-torsion Sylow subgroup, then $\mathbb{Z}[[G]]$ is neither left nor right coherent.

Theorems & Definitions (20)

  • Theorem 1.1
  • Theorem 1.2
  • Proposition 2.1
  • proof
  • Proposition 2.2
  • proof
  • Remark 2.3
  • Corollary 2.4
  • proof
  • Definition 3.1
  • ...and 10 more