Related papers: The pro-$p$ group of upper unitriangular matrices

Let $FG$ be the group algebra of a finite $p$-group $G$ over a finite field $F$ of characteristic $p$ and $*$ the classical involution of $FG$. The $*$-unitary subgroup of $FG$, denoted by $V_*(FG)$, is defined to be the set of all…

If G is a pro-p, p-adic, Lie group and if $\Lambda(G)$ denotes the Iwasawa algebra of G then we present a formula for determining the $\Lambda(G)$-rank of a finitely generated $\Lambda(G)$-module. This is given in terms of the G homology…

Let $\boldsymbol{G}$ be an algebraic group of exceptional Lie type in characteristic $p$, $G=\boldsymbol{G}^{\sigma}$ its fixed-point subgroup under the action of a Steinberg endomorphism $\sigma$, and $\overline{G}$ an almost simple group…

It is known that, if all the real-valued irreducible characters of a finite group have odd degree, then the group has normal Sylow $2$-subgroup. We generalize this result for Sylow $p$-subgroups, for any prime number $p$, while assuming the…

Let p be an odd prime satisfying Vandiver's conjecture. We consider two objects, the Galois group X of the maximal unramified abelian pro-p extension of the compositum of all Z_p-extensions of the pth cyclotomic field and the Galois group G…

Extending some results of a joint work with E. Glasner, we continue to study the Polish group $G:=\mathrm{Aut}(\mathbb{Q}_0)$ of all circular order preserving permutations of the rational circle $\mathbb Q_0=\mathbb Q/\mathbb Z$, endowed…

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…

Let $p$ be a prime number and $\mathbb{Z}_p=\mathbb{Z}/p\mathbb{Z}$. We study finite groups with abelian derived subgroup and exponent $p$ in terms of group extension data and their matrix presentations. We show a one-to-one correspondence…

We study the category of $\mathbf{P}$-equivariant modules over the infinite variable polynomial ring, where $\mathbf{P}$ denotes the subgroup of the infinite general linear group $\mathbf{GL}(\mathbf{C}^\infty)$ consisting of elements…

Let $p$ be a prime, $k$ a finite extension of $\mathbf{F}_p$ of cardinal $q$, $l$ a finite extension of $k$ of group $\Sigma=\mathrm{Gal}(l|k)$, and $T$ a subgroup of $l^\times$. Using the method of "little groups", we classify irreducible…

Let $F$ be a non-Archimedean locally compact field, let $G$ be a split connected reductive group over $F$. For a parabolic subgroup $Q\subset G$ and a ring $L$ we consider the $G$-representation on the $L$-module$$(*)\quad\quad\quad\quad…

We continue the examination of the stable reduction and fields of moduli of G-Galois covers of the projective line over a complete discrete valuation field of mixed characteristic (0, p), where G has a cyclic p-Sylow subgroup P of order…

Let $G$ be a finite group and let $(P_i)_{i=1}^n$ be Sylow subgroups for distinct primes $p_1,\ldots,p_n$. We conjecture that there exists $x \in G$ such that $P_i \cap P_i^x$ is inclusion-minimal in $\{ P_i \cap P_i^g : g \in G\}$ for all…

Let $G$ be any group. The quotient group $T(G)$ of the multiple holomorph by the holomorph of $G$ has been investigated for various families of groups $G$. In this paper, we shall take $G$ to be a finite $p$-group of class two for any odd…

We study basic properties of the category of smooth representations of a p-adic group G with coefficients in any commutative ring R in which p is invertible. Our main purpose is to prove that Hecke algebras are noetherian whenever R is ; a…

Translating results due to J. Labute into group cohomological language, A. Schmidt proved that a finitely presented pro-p-group G is mild and hence of cohomological dimension cd G=2 if $H^1(G,\F_p)=U\oplus V$ as $\F_p$-vector space and the…

We construct Graev ultrametrics on free products of groups with two-sided invariant ultrametrics and HNN extensions of such groups. We also introduce a notion of a free product of general Polish groups and prove, in particular, that two…

Let $k$ be a field and $G$ be a finite group acting on the rational function field $k(x_g : g\in G)$ by $k$-automorphisms defined as $h(x_g)=x_{hg}$ for any $g,h\in G$. We denote the fixed field $k(x_g : g\in G)^G$ by $k(G)$. Noether's…

For a prime number $p$ and a free pro-$p$ group $G$ on a totally ordered basis $X$, we consider closed normal subgroups $G^\Phi$ of $G$ which are generated by $p$-powers of iterated commutators associated with Lyndon words in the alphabet…

We investigate the automorphism group of the quantised enveloping algebra U of the positive nilpotent part of certain simple complex Lie algebras g in the case where the deformation parameter q \in \mathbb{C}^* is not a root of unity.…