Related papers: Counting irreducible modules for profinite groups

We define a class of pre-ordered abelian groups that we call finite-by-Presburger groups, and prove that their theory is model-complete. We show that certain quotients of the multiplicative group of a local field of characteristic zero are…

Finitely generated (non-abelian) free metabelian pro-p groups, and wreath products of f.g. free abelian pro-p groups, are all finitely axiomatizable in the class of all profinite groups.

The structure of finite and locally finite groups in which every element has prime power order (CP-groups) is well known. In this paper we note that the combination of our earlier results with the available information on the structure of…

We completely describe the finitely generated pro-$p$ subgroups of the profinite completion of the fundamental group of an arbitrary $3$-manifold. We also prove a pro-$p$ analogue of the main theorem of Bass--Serre theory for finitely…

A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semibounded if the corresponding operators $i\dd\pi(x)$ from the derived representation are uniformly bounded from above on some non-empty open subset of…

We present novel constructions concerning the homology of finitely generated groups. Each construction draws on ideas of Gilbert Baumslag. There is a finitely presented acyclic group $U$ such that $U$ has no proper subgroups of finite index…

A residually finite (profinite) group $G$ is just infinite if every non-trivial (closed) normal subgroup of $G$ is of finite index. This paper considers the problem of determining whether a (closed) subgroup $H$ of a just infinite group is…

We construct the irreducible unipotent modules of the finite general linear groups using tableaux. Our construction is analogous to that of James (1976) for the symmetric groups, answering an open question as to whether such a construction…

A 1-ended finitely presented group has semistable fundamental group at $\infty$ if it acts geometrically on some (equivalently any) simply connected and locally finite complex $X$ with the property that any two proper rays in $X$ are…

For a residually finite group $G$, its normal subgroups $G\supset G_1\supset G_2\cdots$ with $\cap_{n\in\mathbb N}G_n=\{e\}$ and for a growth function $\gamma$ we construct a unitary representation $\pi_\gamma$ of $G$. For the minimal…

We extend some of our earlier results on the interconnection between ultrafilter extensions, and ultrapowers. Throughout we restrict ourselves to relational structures with one binary relation. Recently it was shown that for bounded…

Let $p$ be an odd prime and $F_\infty$ be a $\mathbb{Z}_p$-extension of a number field $F$. Given an elliptic curve $E$ over $F$, we study the structure of the fine Selmer group over $F_\infty$. It is shown that under certain conditions,…

A global representation is a compatible collection of representations of the outer automorphism groups of the finite groups belonging to a family $\mathscr{U}$. These arise in classical representation theory, in the study of representation…

We prove that if G is a sufficiently large finite almost simple group of Lie type, then given a fixed nontrivial element x in G and a coset of G modulo its socle, the probability that x and a random element of the coset generate a subgroup…

A profinite group G is just infinite if every non-trivial closed normal subgroup of G is of finite index, and hereditarily just infinite if every open subgroup is just infinite. Hereditarily just infinite profinite groups need not be…

We study profinite actions of residually finite groups in terms of weak containment. We show that two strongly ergodic profinite actions of a group are weakly equivalent if and only if they are isomorphic. This allows us to construct…

In this paper we expand on previous results, studying the extent to which one can detect fusion in certain finite groups $\Gamma$, from information about the universal deformation rings of absolutely irreducible…

We use model theory to study relative profinite rigidity of $3$-manifold groups and show that given any residually finite group $\Gamma$ with finite character variety and single-cusped finite volume hyperbolic $3$-manifold $M$, cofinitely…

We give criteria on an inverse system of finite groups that ensure the limit is just infinite or hereditarily just infinite. More significantly, these criteria are 'universal' in that all (hereditarily) just infinite profinite groups arise…

Building on work of J. Robinson and A. Shlapentokh, we develop a general framework to obtain definability and decidability results of large classes of infinite algebraic extensions of $\mathbb{F}_p(t)$. As an application, we show that for…