We give an upper bound of $n((n-1)!-(n-3)!)$ for the possible largest size ofa subsemigroup of the full transformational semigroup over $n$ elementsconsisting only of nonpermutational transformations. As an application we gainthe same upper bound for the syntactic complexity of (generalized) definitelanguages as well.
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机译：对于仅由非置换变换组成的，超过$ n $个元素的完全变换半群的一个亚半群的可能最大大小，我们给出$ n（（n-1）！-（n-3）！）$的上限。作为一种应用程序，我们也为（广义）定语的语法复杂度获得了相同的上限。
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