Related papers: Infinitely Generated virtually free pro-$p$ groups…

In this paper we prove a pro-p version of the Rips-Sela's Theorems on splittings of a group as an amalgamated free product or HNN-extension over an infinite cyclic subgroup.

We determine which faithful irreducible representations $V$ of a simple linear algebraic group $G$ are generically free for Lie($G$), i.e., which $V$ have an open subset consisting of vectors whose stabilizer in Lie($G$) is zero. This…

In this note, we verify that several fundamental results from the theory of representations of reductive $p$-adic groups, extend to finite central extensions of these groups.

We construct a new family of irreducible unitary representations of a finitely generated virtually free group L. We prove furthermore a general result concerning representations of Gromov hyperbolic groups that are weakly contained in the…

For any prime number p and any positive real number {\alpha}, we construct a finitely generated group {\Gamma} with p-gradient equal to {\alpha}. This construction is used to show that there exist uncountably many pairwise non-commensurable…

We define the notion of accessibility for a pro-$p$ group. We prove that finitely generated pro-$p$ groups are accessible given a bound on the size of their finite subgroups. We then construct a finitely generated inaccessible pro-$p$…

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…

For a simple linear algebraic group $G$ acting faithfully on a vector space $V$ and under mild assumptions, we show: if $V$ is large enough, then the Lie algebra of $G$ acts generically freely on $V$. That is, the stabilizer in the Lie…

We show that for every finitely generated closed subgroup $K$ of a non-solvable Demushkin group $G$, there exists an open subgroup $U$ of $G$ containing $K$, and a continuous homomorphism $\tau \colon U \to K$ satisfying $\tau(k) = k$ for…

Let $S$ be either a free group or the fundamental group of a closed hyperbolic surface. We show that if $G$ is a finitely generated residually-$p$ group with the same pro-$p$ completion as $S$, then two-generated subgroups of $G$ are free.…

We define and study a pro-$p$ version of Sidki's weak commutativity construction. This is the pro-$p$ group $\mathfrak{X}_p(G)$ generated by two copies $G$ and $G^{\psi}$ of a pro-$p$ group, subject to the defining relators $[g,g^{\psi}]$…

We initiate the study of some pro-p-groups arising from infinite-dimensional Lie theory. These groups are completions of some subgroups of incomplete Kac-Moody groups over finite fields, with respect to various completions of algebraic or…

It is shown that the relatively free centre-by-metabelian and (class-2 nilpotent)-by-abelian pro-p groups on 2 generators are each finitely axiomatizable in the class of all profinite groups.

Let p be a prime. Uniform pro-p groups play a central role in the theory of p-adic Lie groups. Indeed, a topological group admits the structure of a p-adic Lie group if and only if it contains an open pro-p subgroup which is uniform.…

In the paper we study irreducible representations of some nilpotent groups of finite abelian total rank. The main result of the paper states that if a torsion-free minimax group $G$ of nilpotency class 2 admits a faithful irreducible…

We determine all finite p-groups that admit a faithful, self-similar action on the p-ary rooted tree such that the first level stabilizer is abelian. A group is in this class if and only if it is a split extension of an elementary abelian…

We develop methods to show that infinite-dimensional modules over the Iwasawa algebra $KG$ of a uniform pro-p group are faithful and apply them to show that the metaplectic representation for the symplectic group is faithful.

We prove an accessibility theorem for finite-index splittings of groups. Given a finitely presented group G there is a number n(G) such that, for every reduced locally finite G-tree T with finitely generated stabilizers, T/G has at most…

We prove that for a suitable class of representations of free group tensor products are generically irreducible. In particular we prove that there exist irreducible boundary realizations with infinite dimensional fiber.

Using exceptional theta correspondences, we prove that certain Weil representations of $p$-adic groups are multiplicity free and determine irreducible quotients.