Constructing skew left braces whose additive group has trivial centre

TL;DR

This paper provides a complete classification of finite skew left braces with additive groups having trivial center, improving previous results and answering an open question from a recent conference.

Contribution

It offers a full description of the multiplicative groups of such skew left braces, advancing the understanding of their structure and properties.

Findings

Complete classification of multiplicative groups of skew left braces with trivial center

Improved earlier results of Tsang

Answered an open question from Ischia Group Theory 2024

Abstract

A complete description of all possible multiplicative groups of finite skew left braces whose additive group has trivial centre is shown. As a consequence, some earlier results of Tsang can be improved and an answer to an open question set by Tsang at Ischia Group Theory 2024 Conference is provided.