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We present a generalization of the notion of reduction group which allows one to study in a uniform way certain classes of nonlocal $S$-integrable equations like Ablowitz-Musslimani's nonlocal Schr\"odinger equation. Another aspect of the proposed generalization is the possibility to derive in a systematic way solutions to S-integrable equations with prescribed symmetries.
T. Valchev, On Mikhailov’s reduction group, Physics Letters - A 379 (2015) 1877–1880. doi:10.1016/j.physleta.2015.05.024