Related papers: Full Level Structure on Some Group Schemes

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the…

As well-known, in a finitary algebraic structure the set $\Gamma$ of all the non-generators is the intersection of all the maximal proper substructures. In particular, $\Gamma$ is a substructure. We show that the corresponding statements…

We give a structural theorem for pseudofinite groups of finite centraliser dimension. As a corollary, we observe that there is no finitely generated pseudofinite group of finite centraliser dimension.

In this note, we define a new graph $\Gamma_d(G)$ on a finite group $G$, where $d$ is a divisor of $|G|$. The vertices of $\Gamma_d(G)$ are the subgroups of $G$ of order $d$ and two subgroups $H_1$ and $H_2$ of $G$ are said to be adjacent…

Every mathematician is familiar with the beautiful structure of finite commutative groups. What is less well known is that finite commutative semigroups also have a neat and well-described structure. We prove this in an efficient fashion.…

Let $\sigma =\{\sigma_i |i\in I\}$ is some partition of all primes $\mathbb{P}$ and $G$ a finite group. A subgroup $H$ of $G$ is said to be $\sigma$-subnormal in $G$ if there exists a subgroup chain $H=H_0\leq H_1\leq \cdots \leq H_n=G$…

Decomposable ordered structures were introduced in \cite{OnSt} to develop a general framework to study `finite-dimensional' totally ordered structures. This paper continues this work to include decomposable structures on which a ordered…

To any dg-category $T$ (over some base ring $k$), we define a $D^{-}$-stack $\mathcal{M}_{T}$ in the sense of \cite{hagII}, classifying certain $T^{op}$-dg-modules. When $T$ is saturated, $\mathcal{M}_{T}$ classifies compact objects in the…

We construct equivalences among four notions associated to a reductive group scheme $G$: factorization super central extensions of the loop group of $G$ by $\mathbb G_m$ subject to a condition on the commutator, factorization super line…

Let S be a Noetherian scheme, f:X->Y a surjective S-morphism of S-schemes, with X of finite type over S. We discuss what makes Y of finite type. First, we prove that if S is excellent, Y is reduced, and f is universally open, then Y is of…

Let $\sigma =\{\sigma_{i} | i\in I\}$ be some partition of the set of all primes $\Bbb{P}$. A set ${\cal H}$ of subgroups of $G$ is said to be a \emph{complete Hall $\sigma $-set} of $G$ if every member $\ne 1$ of ${\cal H}$ is a Hall…

We prove that in every finitely generated profinite group, every subgroup of finite index is open; this implies that the topology on such groups is determined by the algebraic structure. This is deduced from the main result about finite…

This article began as a study of the structure of infinite permutation groups G in which point stabilisers are finite and all infinite normal subgroups are transitive. That led to two variations. One is the generalisation in which point…

We give an explicit construction of the antiequivalence of the category of finite flat commutative group schemes of period 2 defined over the valuation ring of a 2-adic field with algebraically closed residue field. This result extends the…

Unique lifting factorization results for group lifting structures are used to characterize the group-theoretic structure of two-channel linear phase FIR perfect reconstruction filter bank groups. For D-invariant, order-increasing group…

Let $G$ be a finite $p$-group of order $p^n$. It is known that $|\mathcal{M}(G)|=p^{\f{1}{2}n(n-1)-t(G)}$ and $t(G)\geq 0$. The structure of $G$ characterized when $t(G)\leq 4$ in \cite{be,el,ni,sa,zh}. The structure description of $G$ is…

Let $k$ be an algebraically closed field of characteristic $0$ or $p>2$. Let $\mathcal{G}$ be an affine supergroup scheme over $k$. We classify the indecomposable exact module categories over the tensor category ${\rm sCoh}_{\rm…

The homology groups introduced by A. Brumer can be used to establish a criterion ensuring that a profinite $\mathbb{F}_p[[G]]$-module of a pro-$p$ group $G$ has projective dimension $d<\infty$ (cf. Thm. A). This criterion yields a new…

Let $G$ be an inner form of a general linear group over a non-archimedean locally compact field of residue characteristic $p$, let $R$ be an algebraically closed field of characteristic different from $p$ and let $\mathscr{R}_R(G)$ be the…

A subshift on a group G is a closed, G-invariant subset of A^G, for some finite set A. It is said to be a subshift of finite type (SFT) if it is defined by a finite collection of 'forbidden patterns', to be strongly aperiodic if all point…