SUBWORD COMPLEXITY OF PROFINITE WORDS AND SUBGROUPS OF FREE PROFINITE SEMIGROUPS
Jorge Almeida, Mikhail Vladimirovich Volkov · International Journal of Algebra and Computation · 2006
We study free profinite subgroups of free profinite semigroups of the same rank using, as main tools, iterated continuous endomorphisms, subword complexity, and the associated entropy. Main results include a general scheme to produce such subgroups and a proof that the complement of the minimal ideal in a free profinite semigroup on more than one generator is closed under all implicit operations that do not lie in the minimal ideal and even under their infinite iteration.