Given a polynomial of degree d over number field, the image associated arboreal representation absolute Galois group field is profinite acting on d-ary tree. Boston and Jones conjectured that for quadratic polynomial, such contains dense set settled elements. Here an element if it exhibits certain pattern growth cycles at finite levels In this paper, we prove conjecture generically in case when...

A profinite group equipped with an expansive endomorphism is equivalent to a one-sided shift. We show that these groups have very restricted structure. More precisely, we any such can be decomposed into finite sequence of full shifts and two groups.

In this paper we determine the automorphism groups of profinite braid with four or more strings in terms Grothendieck-Teichm\"uller group.

For a profinite group, we construct a model structure on profinite spaces with a continuous action. We construct descent spectral sequences for the homotopy groups of the homotopy fixed point space and for the homology of homotopy orbit space which are strongly convergent for an arbitrary profinite group. Our main example is the Galois action on profinite étale topological types of schemes over...

Let R be any ring (with 1), Γ a group and RΓ the corresponding group ring. Let H be a subgroup of Γ of finite index. Let M be an RΓ−module, whose restriction to RH is projective. Moore’s conjecture [5]: Assume for every nontrivial element x in Γ, at least one of the following two conditions holds: M1) 〈x〉 ∩ H 6= {e} (in particular this holds if Γ is torsion free) M2) ord(x) is finite and invert...