Using free profinite semigroupoids generated by Rauzy graphs
to compute J-maximal subgroups of free profinite semigroups
Although free profinite semigroups proved to be a fundamental tool in the study of (pseudovarieties) of finite semigroups, their structure remained until recently significantly obscure. Jorge Almeida proposed to use some tools from symbolic dynamics to study them. In this talk we focus in one of these tools, free profinite semigroupoids generated by Rauzy graphs of subshifts, to enlighten the structure of certain J-classes, specially through the
computation of J-maximal subgroups. In this process, we shall also get a look to the usefulness of these special free profinite
semigroupoids to understand (free) profinite semigroupoids in general.
Alfredo Costa (CMUC/Mat. FCTUC)
January 08, 2008