# Fast detection of giant permutation groups

## TL;DR

This paper introduces a faster randomized algorithm for detecting if a permutation group contains the alternating group, improving upon existing methods and previous algorithms by Cameron and Cannon.

## Contribution

A novel 1-sided randomized algorithm that efficiently detects the presence of the alternating group within permutation groups given by generators.

## Key findings

- Algorithm is faster than standard methods.
- Outperforms previous algorithms by Cameron and Cannon.
- Provides reliable detection with probabilistic guarantees.

## Abstract

We give a 1-sided randomised algorithm to detect when a permutation group of degree n, given by generators, contains the alternating group of degree n. This improves on standard methods, and on an algorithm of P. Cameron and J. Cannon.