On a finite subsemigroup of semigroups in which x^r=x
  In this paper, we consider the following problem: For every positive integer $r \geq 2$, find all positive integers $n$ such that for every semigroup of order $\geq n$ in which $x^r=x$ for every element $x$ has a subsemigroup of order $n$. 
Jungin Lee
math.GR