相关论文: New necessary conditions for Payley type PDS in Ab…

In this paper we give invariants that characterize isotypically equivalent Abelian periodic groups. Also, we describe types of standart tuples of elements in these groups. As the particular case we prove that two Abelian $p$-groups with…

Let G be a connected reductive group defined over an algebraically closed field k of characteristic p > 0. The purpose of this paper is two-fold. First, when p is a good prime, we give a new proof of the ``order formula'' of D. Testerman…

In this paper, we present constructions of abelian Paley type group schemes by using multiplicative characters of finite fields and Arasu-Dillon-Player difference sets. The constructions produce many new Paley type group schemes that were…

The paper studies the minimum polynomial degrees of $p$-elements in cross-characteristic representations of simple groups of exceptional Lie type whose BN-pair rank is at most 2. Specifically, we prove that the degree in question equals the…

Let G be a finite abelian group with |G|>1. Let a_1,...,a_k be k distinct elements of G and let b_1,...,b_k be (not necessarily distinct) elements of G, where k is a positive integer smaller than the least prime divisor of |G|. We show that…

Faltings in 1983 proved that a necessary and sufficient condition for two abelian varieties $A$ and $B$ to be isogenous over a number field $K$ is that the local factors of the L-series of $A$ and $B$ are equal for almost all primes of $K$…

A partial difference set $S$ in a finite group $G$ satisfying $1 \notin S$ and $S = S^{-1}$ corresponds to an undirected strongly regular Cayley graph ${\rm Cay}(G,S)$. While the case when $G$ is abelian has been thoroughly studied, there…

The mininal degree of a finite group G, mu(G), is defined to be the smallest natural number n such that G embeds inside Sym(n). The group G is said to be exceptional if there exists a normal subgroup N such that mu(G/N)>mu(G). We will…

In this paper, using a criterion given by J. Brough and B. Spaeth recently, we verify the inductive blockwise Alperin weight condition for the simple groups PSp2n(q) and any odd prime l not dividing q under some assumptions concerning the…

We consider $p$-blocks with abelian defect groups and in the first part prove a relationship between its Loewy length and that for blocks of normal subgroups of index $p$. Using this, we show that if $B$ is a $2$-block of a finite group…

Combining results on quadrics in projective geometries with an algebraic interplay between finite fields and Galois rings, we construct the first known family of partial difference sets with negative Latin square type parameters in…

We give necessary conditions satisfied by the set of odd prime divisors of binary perfect polynomials. This allows us to get a new characterization of all the known perfect binary polynomials.

We consider the families of finite Abelian groups $\ZZ/p\ZZ\times \ZZ/p\ZZ$, $\ZZ/p^2\ZZ$ and $\ZZ/p\ZZ\times \ZZ/q\ZZ$ for $p,q$ two distinct prime numbers. For the two first families we give a simple characterization of all functions…

Using only undergraduate-level methods, we classify all groups of order $p^4$, where $p$ is an odd prime.

There are several results in the literature concerning $p$-groups $G$ with a maximal elementary abelian normal subgroup of rank $k$ due to Thompson, Mann and others. Following an idea of Sambale we obtain bounds for the number of generators…

In this paper we produce unconditionally new instances of Galois number field extensions exhibiting strong discrepancies in the distribution of Frobenius elements among conjugacy classes of the Galois group. We first prove an inverse Galois…

We prove that there exist infinitely many a non-abelian strongly real Beauville $p$-group for every prime $p$. Previously only finitely many in the case $p=2$ have been constructed.

We determine the non-abelian composition factors of the finite groups with Sylow normalizers of odd order. As a consequence, among others, we prove the McKay conjecture and the Alperin weight conjecture for these groups.

The local invariants of a meromorphic Abelian differential on a Riemann surface of genus $g$ are the orders of zeros and poles, and the residues at the poles. The main result of this paper is that with few exceptions, every pattern of…

We prove the existence of an Abelian variety $A$ of dimension $g$ over $\Qa$ which is not isogenous to any Jacobian, subject to the necessary condition $g>3$. Recently, C.Chai and F.Oort gave such a proof assuming the Andr\'e-Oort…