Locally nilpotent linear groups

TL;DR

This paper surveys locally nilpotent linear groups and introduces a new classification of irreducible maximal locally nilpotent subgroups of general linear groups over fields, focusing on prime dimensions.

Contribution

It provides the first classification of irreducible maximal locally nilpotent subgroups of GL(q, F) for prime q and any field F.

Findings

Classification of irreducible maximal locally nilpotent subgroups of GL(q, F)

New insights into the structure of locally nilpotent linear groups

Extension of classification to arbitrary fields and prime dimensions

Abstract

We survey aspects of locally nilpotent linear groups. Then we obtain a new classification; namely, we classify the irreducible maximal locally nilpotent subgroups of $\mathrm{GL}(q, \mathbb F)$ for prime $q$ and any field $\mathbb F$.