Group theory via global semigroup theory
Groups are shown to be special homomorphic images of residually finite inverse semigroups. To this aim the authors define three types of expansions of semigroups. When the starting semigroup is a group the three types of expansions give isomorphic semigroups and (selecting a large enough generator set for the group) the expansion thus obtained is an inverse semigroup. The results are applied to the Burnside problem and the following proposition is obtained: Let G be a finite group of odd order. Then G is a homomorphic image of a bounded torsion semigroup the finite subgroups of which are cyclic.
scientific article; zbMATH DE number 4093769