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To extend the results related to retractability to non-involutive solutions, following the ideas of Meng, Ballester-Bolinches and Romero, we develop the theory of right [Formula: see text]-nilpotent skew braces. The theory of left [Formula: see text]-nilpotent skew braces is also developed and used to give a short proof of a theorem of Smoktunowicz in the context of skew braces.<\/jats:p>","DOI":"10.1142\/s0218196719500656","type":"journal-article","created":{"date-parts":[[2019,8,26]],"date-time":"2019-08-26T07:56:20Z","timestamp":1566806180000},"page":"91-115","source":"Crossref","is-referenced-by-count":9,"title":["Retractability of solutions to the Yang\u2013Baxter equation and p-nilpotency of skew braces"],"prefix":"10.1142","volume":"30","author":[{"given":"E.","family":"Acri","sequence":"first","affiliation":[{"name":"IMAS\u2013CONICET and Universidad de Buenos Aires, Pabell\u00f3n 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina"}]},{"given":"R.","family":"Lutowski","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, University of Gda\u0144sk, ul. 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