Related papers: Some model theory of profinite groups

In this paper we define and develop the theory of the cohomology of a profinite group relative to a collection of closed subgroups. Having made the relevant definitions we establish a robust theory of cup products and use this theory to…

We solve an open problem of Herfort and Ribes: Profinite Frobenius groups of certain type do occur as closed subgroups of free profinite products of two profinite groups. This also solves a question of Pop about prosolvable subgroups of…

We give some results on a priori estimates and on estimates of type sup+inf and sup*inf.

We describe the ind- and pro- categories of the category of definable sets, in some first order theory, in terms of points in a sufficiently saturated model.

We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of all non exceptional irreducible complex…

We survey recent work ranging around the question in how far a group, or a property of a group, is determined by the set of finite quotient groups. Our focus lies on $S$-arithmetic groups, branch groups, and their relatives.

This is an introduction to the finite groups, with focus on the groups of permutations and reflections, and more generally, on the finite groups of unitary matrices. We first discuss the basics of group theory, featuring the cyclic,…

For a group $G$, a {\it normalizer covering} of $G$ is a finite set of proper normalizers of some subgroups of $G$ whose union is $G$. We study $p$-groups ($p$ a prime) without a normalizer covering. As an application, we determine some…

A pro-p Cappitt group is a pro-p group G such that the subgroup topologically generated by all non-normal closed subgroups is a proper subgroup of G. In this paper we prove that non-abelian pro-p Cappitt groups whose torsion subgroup is…

We develop the local-global theory of blocks for profinite groups. Given a field $k$ of characteristic $p$ and a profinite group $G$, one may express the completed group algebra $k[[G]]$ as a product $\prod_{i\in I}B_i$ of closed…

We define and study a higher-dimensional version of model theoretic internality, and relate it to higher-dimensional definable groupoids in the base theory.

Given a discrete (resp. profinite) group $G$, we define $NCC(G)$ to be the smallest number of cyclic (resp. procyclic) subgroups of $G$ whose conjugates cover $G$. In this paper we determine all residually finite discrete groups with finite…

We introduce the condition of a profinite group being semi-free, which is more general than being free and more restrictive than being quasi-free. In particular, every projective semi-free profinite group is free. We prove that the usual…

We prove that any type in an NIP theory can be decomposed into a stable part (a generically stable partial type) and a distal-like quotient.

The well-known theory of Pontryagin duality provides a strong connection between the homology and cohomology theories of a profinite group in appropriate categories. A construction for taking the `profinite direct sum' of an infinite family…

Groups, in which every subgroup containing some fixed primary cyclic subgroup has a complement, are investigated.

We develop the theory of group graded division ring parallel to the one by P. Cohn for (ungraded) division rings.

This text is an introduction to the study of NIP (or dependent) theories. It is meant to serve two purposes. The first is to present various aspects of NIP theories and give the reader the background material needed to understand almost any…

We include short and elementary proofs of two theorems characterizing reductive group schemes over a discrete valuation ring, in a slightly more general context.

In this article we show how Gr\"un's results in group theory can be used for studying the structure of class groups in normal extensions.