Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

5-Engel Lie algebras

Michael Vaughan-Lee

Abstract

We prove that 5-Engel Lie algebras over a field of characteristic zero, or over a field of prime characteristic $p>7$, are nilpotent of class at most 11. We also prove that if $G$ is a finite 5-Engel $p$-group for $p>7$ then $G$ is nilpotent of class at most 10.

5-Engel Lie algebras

Abstract

We prove that 5-Engel Lie algebras over a field of characteristic zero, or over a field of prime characteristic , are nilpotent of class at most 11. We also prove that if is a finite 5-Engel -group for then is nilpotent of class at most 10.
Paper Structure (7 sections, 3 theorems, 38 equations)

This paper contains 7 sections, 3 theorems, 38 equations.

Table of Contents

  1. Introduction
  2. Free Lie algebras
  3. Lie superalgebras
  4. Representation theory of the symmetric group
  5. Characteristic 11
  6. The calculations
  7. Locally nilpotent 5-Engel groups

Key Result

Theorem 1

If $L$ is a $5$-Engel Lie algebra over a field of characteristic zero, or over a field of prime characteristic $p>7$, then $L$ is nilpotent of class at most $11$.

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2
  • Theorem 3