On the Classification of Finite Semigroups and RA-loop with the Hyperbolic Property

Abstract

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.

5 pages; this is part of the second and third chapters of the second author's PhD. Thesis. The last theorem was revised, as well as added some definitions and references