A Counterexample to Byott's Conjecture for Finite Skew Braces

Massimiliano Di Matteo; Maria Ferrara; Marco Trombetti

A Counterexample to Byott's Conjecture for Finite Skew Braces

Group Theory 2026-07-24 v1 Rings and Algebras

Authors: Massimiliano Di Matteo , Maria Ferrara , Marco Trombetti

Abstract

We construct a finite skew brace with soluble additive group and insoluble multiplicative group. The multiplicative group has a quotient isomorphic to $\PSL_2(7)$ , and hence the example disproves Byott's conjecture.

Keywords

skew brace finite skew brace additive group multiplicative group PSL_2(7)

Cite

@article{arxiv.2607.22795,
  title  = {A Counterexample to Byott's Conjecture for Finite Skew Braces},
  author = {Massimiliano Di Matteo and Maria Ferrara and Marco Trombetti},
  journal= {arXiv preprint arXiv:2607.22795},
  year   = {2026}
}

Comments

15pp