Quasigroups, Units and Belousov’s Problem # 18 - Krapež, Aleksandar; Shcherbacov, Victor A. (Armenian Journal of Mathematics, 2019)
We investigate left, right, middle} units of quasigroups and families of identities which might imply their existence. A prominent role is played by the newly introduced notion of derivative operation, generalizing Belousov’s notions of left/right derivative operations for quasigroups. Partial solutions of the Belousov’s Problem # 18 and its generalizations are obtained. Several related problems remain open.