Efficient characteristic refinements for finite groups

TL;DR

This paper introduces an efficient algorithm for characteristic refinements in finite groups, enhancing computational methods and demonstrating practical usefulness on $p$-groups, with potential applications in group isomorphism testing.

Contribution

It provides a practical, efficient algorithm for characteristic refinements in finite groups, improving upon previous impractical formulas and enabling better computational group analysis.

Findings

Algorithm significantly speeds up characteristic refinement computations.

Demonstrates effectiveness on multiple $p$-group examples.

Potential to improve isomorphism testing methods.

Abstract

Filters were introduced by J.B. Wilson in 2013 to generalize work of Lazard with associated graded Lie rings. It holds promise in improving isomorphism tests, but the formulas introduced then were impractical for computation. Here, we provide an efficient algorithm for these formulas, and we demonstrate their usefulness on several examples of $p$-groups.