Rota-Baxter systems and skew trusses

As a generalization of skew braces, the notion trusses was introduced by T. Brzeziński. It shown that every Rota-Baxter group has structure braces V. G. Bardakov and Gubarev. To investigate an analogue groups which trusses, we define systems. We study relationship between systems groups. Furthermore, prove system can be decomposed as direct sum two semigroups. A factorization theorem is proved, generalizing The Lie algebras introduced, algebras. connection studied. Finally, modified Yang-Baxter equation, twisted equations. give solutions equations