Creating a dynamic database of finite groups

TL;DR

This paper introduces a new dynamic database of finite groups integrated into the LMFDB, highlighting its unique features, challenges faced during development, and its connections to other mathematical objects.

Contribution

It presents the creation and functionality of a comprehensive finite groups database within LMFDB, emphasizing its distinctiveness and integration with existing collections.

Findings

Successfully implemented a dynamic finite groups database

Identified solutions to mathematical challenges in database creation

Established connections between groups and other mathematical objects

Abstract

A database of abstract groups has been added to the L-functions and Modular Forms Database (LMFDB), available at https://www.lmfdb.org/Groups/Abstract/. We discuss the functionality of the database and what makes it distinct from other available databases of abstract groups. We describe solutions to mathematical problems we encountered while creating the database, as well as connections between the abstract groups database and other collections of objects in the LMFDB.