A fast isomorphism test for groups of genus 2

TL;DR

This paper introduces a polynomial-time algorithm for testing isomorphism in a specific class of finite groups, enhancing the efficiency of analyzing local properties of general finite groups, with practical implementation results.

Contribution

The paper presents a novel, efficient isomorphism testing algorithm for a particular class of groups, with implementation in Magma demonstrating its practicality.

Findings

Algorithm runs in polynomial time

Implementation in Magma shows good performance

Applicable to studying local properties of finite groups

Abstract

Motivated by the need for efficient isomorphism tests for finite groups, we present a polynomial-time method for deciding isomorphism within a class of groups that is well-suited to studying local properties of general finite groups. We also report on the performance of an implementation of the algorithm in the computer algebra system {\sc magma}.