Related papers: On hereditarily self-similar $p$-adic analytic pro…

We prove some conditions for higher dimensional algebraic fibering of pro-$p$ group extensions and we establish corollaries about incoherence of pro-$p$ groups. In particular, if $G = K \rtimes \Gamma$ is a pro-$p$ group, $\Gamma$ a…

Let G be a compact, locally L-analytic group, where L is a finite extension of Qp. Let K be a discretely valued extension field of L. We study the algebra D(G,K) of K-valued locally analytic distributions on G, and apply our results to the…

We prove that the geometric etale fundamental group of a (geometrically connected) rigid smooth $p$-adic affinoid curve is a semi-direct factor of a certain profinite free group. We also prove that the maximal pro-$p$ (resp. maximal…

We examine the first non-vanishing higher homotopy group, $\pi_p$, of the complement of a hypersolvable, non--supersolvable, complex hyperplane arrangement, as a module over the group ring of the fundamental group, $\Z\pi_1$. We give a…

Let $G$ be a finite group and $N(G)$ be the set of conjugacy class sizes of $G$. For a prime $p$, let $|G||_p$ be the highest $p$-power dividing some element of $N(G)$. and define $|G|| = {\Pi}_{p\in {\pi}(G)}|G||_p$. $G$ is said to be an…

We show that finite quasisimple groups of Lie type in characteristic $p$ with an irreducible representation of prime degree $r$ over a finite field of characteristic $p$ have orders bounded above by a function of $r$, independent of $p$. We…

Let k be a non-archimedean local field with residual characteristic p. Let G be a connected reductive group over k that splits over a tamely ramified field extension of k. Suppose p does not divide the order of the Weyl group of G. Then we…

We equip the type $A$ diagrammatic Hecke category with a special derivation, so that after specialization to characteristic $p$ it becomes a $p$-dg category. We prove that the defining relations of the Hecke algebra are satisfied in the…

We use a version of Haboush's theorem over complete local Noetherian rings to prove faithfulness of the lifting for semisimple cosemisimple Hopf algebras and separable (braided, symmetric) fusion categories from characteristic $p$ to…

Let $E$ be an elliptic curve---defined over a number field $K$---without complex multiplication and with good ordinary reduction at all the primes above a rational prime $p \geq 5$. We construct a pairing on the dual $p^\infty$-Selmer group…

Let L be a finite extension of Qp, and let K be a spherically complete non-archimedean extension field of L. In this paper we introduce a restricted category of continuous representations of locally L-analytic groups G in locally convex…

For each prime $p$ we construct a family $\{G_i\}$ of finite $p$-groups such that $|\Aut (G_i)|/|G_i|$ goes to $0$, as $i$ goes to infinity. This disproves a well-known conjecture that $|G|$ divides $|\Aut(G)|$ for every non-abelian finite…

We prove that the reduced group C*-algebras of infinite countable discrete groups having topologically-free extreme boundaries, or more generally groups that satisfy certain combinatorial property including all acylindrically hyperbolic…

Suppose that $\mathbf{G}$ is a connected reductive group over a finite extension $F/\mathbb{Q}_p$, and that $C$ is a field of characteristic $p$. We prove that the group $\mathbf{G}(F)$ admits an irreducible admissible supercuspidal, or…

Let $p$ be a prime number. A longstanding conjecture asserts that every finite non-abelian $p$-group has a non-inner automorphism of order $p$. In this paper, we prove that if $G$ is an odd order finite non-abelian monolithic $p$-group such…

We prove pointwise and maximal ergodic theorems for probability measure preserving (p.m.p.) actions of any countable group, provided it admits an essentially free, weakly mixing amenable action of stable type $III_1$. We show that this…

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 $[g,g^{\psi}]$…

According to Li, Nicholson and Zan, a group $G$ is said to be morphic if, for every pair $N_{1}, N_{2}$ of normal subgroups, each of the conditions $G/N_{1} \cong N_{2}$ and $G/N_{2} \cong N_{1}$ implies the other. Finite, homocyclic…

We present a class of abelian groups that exhibit a high degree of freeness while possessing no non-trivial homomorphisms to a canonical free object. Unlike prior investigations, which primarily focused on torsion-free groups, our work…

Let $\mathfrak F$ be a locally compact nonarchimedean field with residue characteristic $p$ and $G$ the group of $\mathfrak{F}$-rational points of a connected split reductive group over $\mathfrak{F}$. We define a torsion pair in the…