Primitive finite nilpotent linear groups over number fields

TL;DR

This paper characterizes finite nilpotent groups that can act primitively as linear groups over a specific number field, using arithmetic invariants of the field to determine primitivity.

Contribution

It provides a precise classification of primitive finite nilpotent linear groups over number fields based on arithmetic conditions, extending previous work on primitivity testing.

Findings

Identifies arithmetic conditions for primitivity over number fields

Classifies finite nilpotent groups that can act primitively

Extends primitivity testing to broader class of fields

Abstract

Building upon the author's previous work on primitivity testing of finite nilpotent linear groups over fields of characteristic zero, we describe precisely those finite nilpotent groups which arise as primitive linear groups over a given number field. Our description is based on arithmetic conditions involving invariants of the field.