On virtually projective groups

TL;DR: In this article, a connection between p-adic representations of finite p-groups and virtually free pro-p groups is explored, and it is shown that a p-group with torsion elements having a finite centralizer is free.

TL;DR: A subgroup of a pro-p product with amalgamation of two p-groups is given in this paper, which cannot be presented as the fundamental group of a profinite graph of p groups.

TL;DR: In this article, it was shown that a second countable torsion free pro-p group G having an open subgroup H that splits as a free pro p product of indecomposable pro p groups is again a free p product.

TL;DR: In this article, the authors classify quadratic, biquadratic and degree 4 cyclic 2-rational number fields with Galois over Q and a degree 2 extension, and explicitly describe the Galois group of their maximal pro-2 extension.

TL;DR: Profinite groups book provides a comprehensive overview of the subject with accessible major theorems and minimal prerequisites.

TL;DR: In this article, the authors proved two conjectures on pro-p groups made by Herfort, Ribes and Zalesskii, and used cohomology to prove the Brown theorem for profinite groups.

TL;DR: In this article, necessary and sufficient conditions for the problem to be Noetherian (i.e. for the operator to be Fredholm) in terms of the invertibility of an auxiliary functional operator acting in a function space on the bundle of unit cotangent vectors to the boundary are presented.