Rewriting the check of 8-rewritability for $A_5$

TL;DR

This paper independently verifies that the alternating group A_5 is 8-rewritable using GAP, comparing the efficiency of sequential and parallel algorithms against previous computational results.

Contribution

It provides an independent computational verification of A_5's 8-rewritability and analyzes the performance of different algorithm implementations.

Findings

Confirmed A_5 is 8-rewritable using GAP

Parallel implementation improves computational efficiency

Comparison with previous methods shows performance gains

Abstract

The group $G$ is called $n$-rewritable for $n>1$, if for each sequence of $n$ elements $x_1, x_2, \dots, x_n \in G$ there exists a non-identity permutation $\sigma \in S_n$ such that $x_1 x_2 \cdots x_n = x_{\sigma(1)} x_{\sigma(2)} \cdots x_{\sigma(n)}$. Using computers, Blyth and Robinson (1990) verified that the alternating group $A_5$ is 8-rewritable. We report on an independent verification of this statement using the computational algebra system GAP, and compare the performance of our sequential and parallel code with the original one.