In "Monoids acting on trees: elliptic and Wreath
products and the holonomy theorem for arbitrary monoids
with application to infinite groups" by the author in
IJAC (vol 1, 1991, pp. 255-279) it was proposed how
global semigroup theory could be applied to infinite groups.
In this talk we carry out the program first for the free groups and then for finitely generated groups. Lots of pictures will be displayed to illustrate the algebraic technique and relate this approach to combinatorial group theory and to R. Grigorchuk's approach to infinite groups via branching groups.
Sponsored in part by the FCT approved projects POCTI 32817/99 and POCTI/MAT/37670/2001 in participation with the European Community Fund FEDER and by FCT through Centro de Matemática da Universidade do Porto. Also sponsored in part by FCT, the Faculdade de Ciências da Universidade do Porto, Programa Operacional Ciência, Tecnologia, Inovação do Quadro Comunitário de Apoio III, and by Caixa Geral de Depósitos.