Related papers: Unipotent elements in small characteristic, II

Let $p$ be a an odd prime and let $G$ be a finite $p$-group with cyclic commutator subgroup $G'$. We prove that the exponent and the abelianization of the centralizer of $G'$ in $G$ are determined by the group algebra of $G$ over any field…

In this paper, we investigate structural properties of finite groups that are detected by certain group invariants arising from Dijkgraaf--Witten theory, a topological quantum field theory, in one space and one time dimension. In this…

This paper consists of two parts. In the first part we show that any Poisson algebraic group over a field of characteristic zero and any Poisson Lie group admits a local quantization. This answers positively a question of Drinfeld. In the…

We introduce {\em admissible collections} for a finite group $G$ and use them to prove that most of the finite classical groups in non-defining characteristic satisfy the {\em Quillen dimension at $p$ property}, a strong version of…

Let $G$ be a multiplicative subgroup of $\mathbb{Q}_p$. In this paper, we describe the theory of the pair $(\mathbb{Q}_p, G)$ under the condition that $G$ satisfies Mann property and is small as subset of a first-order structure. First, we…

We characterize characteristic polynomials of elements in a central simple algebra. We also give an account for the theory of rational canonical forms for separable linear transformations over a central division algebra, and a description…

We give an affrmative answer to the question whether a residually finite Engel group satisfying an identity is locally nilpotent. More generally, for a residually finite group G with an identity, we prove that the set of right Engel…

We show that when G is a finite group which contains an elementary Abelian subgroup of order p^2 and k is an algebraically closed field of characteristic p, then the study of simple endotrivial kG-modules which are not monomial may be…

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…

This survey article is an introduction to some of Lusztig's work on the character theory of a finite group of Lie type $G(F_q)$, where $q$ is a power of a prime~$p$. It is partly based on two series of lectures given at the Centre Bernoulli…

We consider the problem of defining polynomials over function fields of positive characteristic. Among other results, we show that the following assertions are true. 1. Let $\G_p$ be an algebraic extension of a field of $p$ elements and…

Given a finite group $G$ and a prime $p$, let $\mathcal{A}_p(G)$ be the poset of nontrivial elementary abelian $p$-subgroups of $G$. The group $G$ satisfies the Quillen dimension property at $p$ if $\mathcal{A}_p(G)$ has non-zero homology…

Let $G$ be a simple algebraic group of exceptional type over an algebraically closed field of characteristic $p > 0$. This paper continues a long-standing effort to classify the connected reductive subgroups of $G$. Having previously…

Let G be a semi-simple algebraic group over a finitely generated field K of characteristic zero, and let \Gamma < G(K) be a finitely generated Zariski-dense subgroup. In this note we prove that the set of K-generic elements of \Gamma (whose…

For a finite group $G$ and an element $x\in G$, the subset $$ nil_G(x)=\{y\in G \mid <x,y>~~ is ~~ nilpotent\}$$ is called nilpotentizer of $x$ in $G$. In this paper, we give two solvabilty criteria for a finite group by the structure and…

Let $G$ be a $(2,m,n)$-group and let $x$ be the number of distinct primes dividing $\chi$, the Euler characteristic of $G$. We prove, first, that, apart from a finite number of known exceptions, a non-abelian simple composition factor $T$…

We establish some results on the structure of the geometric unipotent radicals of pseudo-reductive k-groups. In particular, our main theorem gives bounds on the nilpotency class of geometric unipotent radicals of standard pseudo-reductive…

Let $G$ be a connnected, unipotent, perfect group scheme over an algebraically closed field of characteristic p > 0. V. Drinfeld has defined a certain metric group associated to biextensions of $G \times G$ by the discrete group $Q_p/Z_p$.…

We define and study supercharacters of the classical finite unipotent groups of symplectic and orthogonal types (over any finite field of odd characteristic). We show how supercharacters for groups of those types can be obtained by…

A criterion is given which assures that two p-divisible groups X and Y over an algebraically closed field of characteristic p are isomorphic when their p-kernels X[p] and Y[p] are isomorphic.