Gr\"obner bases for p-group algebras

TL;DR

This paper investigates how different monomial orderings affect the size of Gr"obner bases in p-group algebras, revealing that reverse length-lexicographical order often produces smaller bases, with Jennings ordering providing a group-invariant algebra.

Contribution

It demonstrates the impact of word ordering choices on Gr"obner basis size in p-group algebras and introduces Jennings ordering as a group-invariant alternative.

Findings

Reverse length-lexicographical order yields smaller Gr"obner bases.

Jennings ordering produces a group-invariant monomial algebra.

Experimental results support the ordering effects on basis size.

Abstract

Experiment shows that the reverse length-lexicographical word ordering consistently yields far smaller Gr\"obner bases for modular p-group algebras than the length-lexicographical ordering. For the so-called Jennings word ordering, based on a special power-conjugate group presentation, the associated monomial algebra is a group invariant.