Indecomposable involutive set-theoretical solutions to the Yang–Baxter equation of size p ²

This article focuses on indecomposable involutive non-degenerate set-theoretical solutions to the Yang–Baxter equation. More specifically, we give a full classification of those solutions which are of size p2, for p a prime. We do this through a thorough analysis of their associated permutation braces and using the language of cycle sets.