The Berman Conjecture Is True for Finite Surjective Semigroups and Their Inflations

A semigroup S is called surjective if S ² =S . The aim of this paper is to prove that p _n -sequences of finite surjective semigroups are eventually strictly increasing, except in few well known cases, when they are bounded. Also, some further types of finite semigroups, obtained by means of subdirect products, are shown to have the same property.