Related papers: On Profinite Quandles
The sets of closed and closed-normal subgroups of a profinite group carry a natural profinite topology. Through a combination of algebraic and topological methods the size of these subgroup spaces is calculated, and the spaces partially…
We propose and develop a theory that allows to characterize epimorphisms of profinite groups in terms of indecomposable epimorphisms.
In this paper we investigate some properties of the Burnside ring of a profinite group as defined in \cite{ds}. We introduce the notion of the crossed Burnside ring of a profinite FC-group, and generalise some results from finite to…
Profinite etale cobordism is a cohomology theory for smooth schemes of finite type over a field. Using an idea of Friedlander, it is constructed as an etale topological analog of the algebraic cobordism theories of Voevodsky and…
In this paper we study some consequences of the author's classification of graph manifolds by their profinite fundamental groups. In particular we study commensurability, the behaviour of knots, and relation to mapping classes. We prove…
Profinite congruences on profinite algebras determining profinite quotients are difficult to describe. In particular, no constructive description is known of the least profinite congruence containing a given binary relation on the algebra.…
In this paper we define the pro-\'etale homotopy type of a scheme and prove some of its expected properties. Our definition is similar to the definition of the \'etale homotopy type by Michael Artin and Barry Mazur. We prove that for a qcqs…
Necessary and sufficient conditions are given for the endomorphism monoid of a profinite semigroup to be profinite. A similar result is established for the automorphism group.
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…
Broadly speaking, a finiteness property of groups is any generalisation of the property of having finite order. A large part of infinite group theory is concerned with finiteness properties and the relationships between them. Profinite…
This article explores the interplay between the finite quotients of finitely generated residually finite groups and the concept of amenability. We construct a finitely generated, residually finite, amenable group $A$ and an uncountable…
This paper establishes strong profinite rigidity results for K\"ahler groups, showing that certain groups are determined within the class of residually finite K\"ahler groups by their profinite completion. Examples include products of…
There has been much recent interest into those properties of a 3-manifold determined by the profinite completion of its fundamental group. In this paper we give readily computable criteria specifying precisely when two orientable graph…
A survey of recent results about profinite groups, and results about infinite and finite groups where the theory of profinite groups plays a leading role.
Surface groups are determined among limit groups by their profinite completions. As a corollary, the set of surface words in a free group is closed in the profinite topology.
We generalise to profinite groups some of our previous results on the cohomology of pro-p groups of bounded sectional p-rank.
This paper summarizes substantive new results derived by a student team (the first three authors) under the direction of the fourth author at the 2005 session of the KSU REU ``Brainstorming and Barnstorming''. The main results are a…
Solid abelian groups, as introduced by Dustin Clausen and Peter Scholze, form a subcategory of all condensed abelian groups satisfying some ''completeness'' conditions and having favourable categorical properties. Given a profinite ring…
We prove that there exist finitely presented, residually finite groups that are profinitely rigid in the class of all finitely presented groups but not in the class of all finitely generated groups. These groups are of the form $\Gamma…
We give necessary and sufficient conditions on the graph of a right-angled Artin group that determine whether the group is subgroup separable or not. Moreover, we investigate the profinite topology of the direct product of two free groups.…