For a given integer
$n = p_1^{\alpha _1 } p_2^{\alpha _2 } \cdots p_k^{\alpha _k }$
(k ≥ 2), we give here a class of finitely presented finite monoids of order n. Indeed the monoids Mon(π), where
$$\pi = {\langle {a_1 ,a_2 , \ldots ,a_k |a_i^{p_i^{\alpha _i } } = {a_i}, {\left({i = 1,2, \ldots ,k} \right)}, a_i a_{i + 1} = {a_i}, \left({i = 1,2, \ldots ,k - 1} \right)} \rangle} .$$
As a result of this study we are able to classify a wide family of the k-generated p-monoids (finite monoids of order a power of a prime p). An interesting di erence between the center of finite p-groups and the center of finite p-monoids has been achieved as well. All of these monoids are regular and non-commutative.