In this paper we consider the semigroup M n of all monotone transformations on the chain X n under the operation of composition of transformations. First we give a presentation of the semigroup M n and some propositions connected with its structure. Also, we give a description and some properties of the classJ n−1 of all monotone transformations with rank n − 1. After that we characterize the maximal subsemigroups of the semigroup M n and the subsemigroups of M n which are maximal inJ n−1 .

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