On groups of I-type and involutive Yang–Baxter groups

We suggest a cohomological framework to describe groups of I-type and involutive Yang–Baxter groups. These groups are key in the study of involutive non-degenerate set-theoretic solutions of the quantum Yang–Baxter equation. Our main tool is a lifting criterion for 1-cocycles, established here in a general non-abelian setting.