Classification of cyclic braces

Etingof, Schedler, and Soloviev have shown [P. Etingof, T. Schedler, A. Soloviev, Set-theoretical solutions to the quantum Yang–Baxter equation, Duke Math. J. 100 (1999) 169–209] that T-structures on cyclic groups come from bijective 1-cocycles and thus give rise to solutions of the quantum Yang–Baxter equation. At the end of their paper, they ask for a classification of T-structures on cyclic groups, especially pp-groups. We solve the latter problem by means of generalized radical rings (=braces).