Locally compact groups built up from p-adic Lie groups, for p in a given set of primes

On the self-similarity index of $p$-adic analytic pro-$p$ groups

Let $p$ be a prime. We say that a pro-$p$ group is self-similar of index $p^k$ if it admits a faithful self-similar action on a $p^k$-ary regular rooted tree such that the action is transitive on the first level. The self-similarity index of a self-similar pro-$p$ group $G$ is defined to be the least power of $p$, say $p^k$, such that $G$ is self-similar of index $p^k$. We show that for every prime $p\geqslant 3$ and all integers $d$ there exist infinitely many pairwise non-isomorphic self-similar 3-dimensional hereditarily just-infinite uniform pro-$p$ groups of self-similarity index greater …

Extensions of the representation modules of a prime order group

For the ring R of integers of a ramified extension of the field of p-adic numbers and a cyclic group G of prime order p we study the extensions of the additive groups of R-representations modules of G by the group G.

具有阿贝尔李代数的单p-进李群

Simple $p$-adic Lie groups with abelian Lie algebras

本文首次构造了任意素数p和正整数d下具有阿贝尔李代数的第二可数拓扑单p-进李群，回答了Glöckner与Caprace-Monod的若干问题，其证明推广了小消去方法至acylindrically hyperbolic群的中心扩张。

Cohomology of uniserial $p$-adic space groups

We prove the non-twisted case of Carlson's conjecture for any prime and we show how to proceed in the twisted case.

Polynomial maps over $p$-adics and residual properties of mapping tori of group endomorphisms

We continue our study of residual properties of mapping tori of free group endomorphisms. In this paper, we prove that each of these groups are virtually residually (finite $p$)-groups for all but finitely many primes$p$. The method involves further studies of polynomial maps over finite fields and $p$-adic completions of number fields.

Modular representations arising from self-dual $\ell$-adic representations of finite groups

Suppose $\ell$ is a prime number, ${\mathbf Q}_\ell$ is the field of $\ell$-adic numbers, ${\mathbf F}_\ell$ is the finite field of $\ell$ elements, and $d$ is a positive integer. Suppose $G$ is a finite subgroup of a symplectic group $Sp_{2d}({\mathbf Q}_\ell)$. We prove that $G$ can be embedded in $Sp_{2d}({\mathbf F}_\ell)$ in such a way that the characteristic polynomials are preserved (mod $\ell$), as long as $\ell>3$.