Related papers: Some questions about representations of p-adic gro…

We give some background on uniform pro-p groups and the model theory of profinite NIP groups.

We survey some results on toric topology.

Consideration of certain properties of group rings and their ideals search

Some aspects of analysis involving fields with absolute value functions are discussed, which includes the real or complex numbers with their standard absolute values, as well as ultrametric situations like the p-adic numbers.

Presentations for the holomorphs of abelian groups of the form $C_{p^n} \times 1^{m}$ for $p$=2 or an odd prime are given. These presentations extend the results given in Burnside's well-known text on finite groups on the holomorphs for the…

These are expanded notes of some lectures given by the author for a workshop held at the Indian Statistical Institute, Bangalore in June, 2010, giving an exposition on the modular representations of finite groups of Lie type and $p$-adic…

We study the representation theory of the fundamental group of the complement of a Hopf link with n twists. A general framework is described to analyze the $SL_r(C)$-representation varieties of these twisted Hopf links as byproduct of a…

In this brief note, we consider p-adic unit roots or poles of L-functions of exponential sums defined over finite fields. In particular, we look at the number of unit roots or poles, and a congruence relation on the units. This raises a…

We describe a geometric counterpart of the Baum-Connes map for the p-adic group GL(n).

This survey article, is written as an extended note and supplement of my lectures in the current developments in mathematics conference in 2015. We discuss some recent developments on the conjugacy classes of affine Weyl groups and $p$-adic…

The group ring of the automorphism group of a p-group is studied using the automorphism groups of subgroups and quotient groups of P.

We state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.

We prove surjectivity criteria for $p$-adic representations and we apply them to abelian varieties over number fields. In particular, we provide examples of Jacobians over $\dbQ$ of dimension $d\in\{1,2,3\}$ whose 2-adic representations…

In this paper, we describe the set of all solutions of monomial equation $x^k=a$ over $\mathbb Q_p$. Moreover, as an application of the result, we study several perturbations of the considered equation over $p$-adic field.

For weighted group convoltion measure algebra we construct a representation on reflexsive space.

We describe an linear representation for Abel-Grassmann groups. As a consequence, we obtain or improve many previous results. In particular, enumeration of Abel-Grassmann groups up to isomorphism is obtained for orders <512.

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…

This article is a survey on the braid groups, the Artin groups, and the Garside groups. It is a presentation, accessible to non-experts, of various topological and algebraic aspects of these groups. It is also a report on three points of…

This is an introduction to the finite groups, with focus on the groups of permutations and reflections, and more generally, on the finite groups of unitary matrices. We first discuss the basics of group theory, featuring the cyclic,…

We describe the Sylow $p$-groups of the group of polynomial permutations of the integers mod $p^n$.