Frobenius Subgroups of Free Profinite Products

Prosolvable Subgroups of Free Products of Profinite Groups

Subword Complexity of Profinite Words and Subgroups of Free Profinite Semigroups

We study free profinite subgroups of free profinite semigroups of the same rank using, as main tools, iterated implicit operators, subword complexity and the associated entropy.

Closed Subgroups of G(Q) with Involutions

The aim of this note is to determine certain closed subgroups of the absolute Galois group G(Q) of Q, in particular subgroups generated by involutions (=elements of order 2). Geyer [3,4.1] has shown, in a far more general set-up, that subgroups generated by finitely many involutions are almost always free profinite products of copies of Z/22. To be precise, fix an involution E E G(Q); for almos...

Rational Codes and Free Profinite Monoids

It is well known that clopen subgroups of finitely generated free profinite groups are again finitely generated free profinite groups. Clopen submonoids of free profinite monoids need not be finitely generated nor free. Margolis, Sapir and Weil proved that the closed submonoid generated by a finite code (which is in fact clopen) is a free profinite monoid generated by that code. In this note we...

Profinite Topologies in Free Products of Groups

Let H be an abstract group and let C be a variety of finite groups (i.e., a class of finite groups closed under taking subgroups, quotients and finite direct products); for example the variety of all finite p-groups, for a fixed prime p. Consider the smallest topology on H such that all the homomorphism H −→ C from H to any group C ∈ C (endowed with the discrete topology) is continuous. We refe...