Maximal finite subgroups and minimal classes

TL;DR

This paper uses Voronoi's algorithm to classify maximal finite subgroups of unit groups in certain algebraic structures, aiding in distinguishing non-isomorphic orders by their unit groups.

Contribution

It applies Voronoi's algorithm to compute conjugacy class representatives of maximal finite subgroups in algebraic unit groups, providing a method to differentiate orders.

Findings

Computed conjugacy classes of maximal finite subgroups in specific cases

Demonstrated non-isomorphic orders have non-isomorphic unit groups in small cases

Provided a computational approach for classifying unit groups

Abstract

We apply Voronoi's algorithm to compute representatives of the conjugacy classes of maximal finite subgroups of the unit group of a maximal order in some simple $\QQ $-algebra. This may be used to show in small cases that non-conjugate orders have non-isomorphic unit groups.