On the Classification of Finite Semigroups and RA-loop with the   Hyperbolic Property
  We classify the finite semigroups S, for which all the Z-orders O of the rational Q-algebra QS, is such that the unit group U(O) is hyperbolic. We also classify the RA-loops L, for which the unit loop U(ZL) does not contain any free abelian subgroup of rank two. 
S.O. Juriaans, A.C. Souza Filho