On complexity of multiplication in finite soluble groups

TL;DR

This paper establishes an upper bound on the computational complexity of multiplying two elements in finite soluble groups using specific polycyclic presentations, aiding understanding of their algebraic structure.

Contribution

It provides a new upper bound for the multiplication complexity in finite soluble groups based on particular polycyclic presentations.

Findings

Derived an explicit upper bound for multiplication complexity.

Focused on polycyclic presentations to analyze computational aspects.

Enhanced understanding of algorithmic efficiency in finite soluble groups.

Abstract

We determine a reasonable upper bound for the complexity of collection from the left to multiply two elements of a finite soluble, or polycyclic, group by restricting attention to certain polycyclic presentations of the group.