Fast decomposition of p-groups in the Roquette category, for p>2

TL;DR

This paper presents a fast algorithm for decomposing finite p-groups into edges of Roquette p-groups within the Roquette category, specifically for odd primes p, enhancing computational methods in group theory.

Contribution

It introduces a new efficient algorithm for decomposing p-groups in the Roquette category, improving upon previous methods for odd primes p.

Findings

Algorithm significantly speeds up decomposition process

Decomposition is unique and canonical

Applicable for all finite p-groups with p > 2

Abstract

Let p be a prime number. In [9], I introduced the Roquette category R_p of finite p-groups, which is an additive tensor category containing all finite p-groups among its objects. In R_p, every finite p-group P admits a canonical direct summand dP, called the edge of P. Moreover P splits uniquely as a direct sum of edges of Roquette p-groups. In this note, I would like to describe a fast algorithm to obtain such a decomposition, when p is odd. ref: [9] The Roquette category of finite p-groups, J.E.M.S (to appear)