Related papers: Generalized Dedekind's theorem and its application…

Building upon the work of Stucker, Vennos, and Young we derive generalized Dedekind sums arising from period integrals applied to holomorphic Eisenstein series attached to pairs of primitive non-trivial Dirichlet characters. Furthermore, we…

For each member $\mathcal{A}$ of a family of linear cycle sets whose underlying abelian group is cyclic of order a power of a prime number, we compute all the central extensions of $\mathcal{A}$ by an arbitrary abelian group.

Let $R$ be a finite commutative ring with identity and $U(R)$ be its group of units. In 2005, El-Kassar and Chehade presented a ring structure for $U(R)$ and as a consequence they generalized this group of units to the generalized group of…

The Steinitz class of a number field extension K/k is an ideal class in the ring of integers O_k of k, which, together with the degree [K:k] of the extension determines the O_k-module structure of O_K. We call R_t(k,G) the classes which are…

This paper contains a stronger version of a final identification theorem for the `generic' groups of finite Morley rank.

Let $G_n$ denote either the group $SO(2n+1, F)$, $Sp(2n, F)$, or $GSpin(2n+1, F)$ over a non-archimedean local field of characteristic different than two. We determine all composition factors of degenerate principal series of $G_n$, using…

We examine the existence of universal elements in classes of infinite abelian groups. The main method is using group invariants which are defined relative to club guessing sequences. We prove, for example: Theorem: For $n\ge 2$, there is a…

We compute bilinear integrals involving Macdonald and Gegenbauer functions. These integrals are convergent only for a limited range of parameters. However, when one uses generalized integrals they can be computed essentially without…

We construct an extension $E(A,G)$ of a given group $G$ by infinite non-Archimedean words over an discretely ordered abelian group like $Z^n$. This yields an effective and uniform method to study various groups that "behave like $G$". We…

In this note we provide some counterexamples for the conjecture of Moret\'{o} on finite simple groups, which says that any finite simple group $G$ can determined in terms of its order $|G|$ and the number of elements of order $p$, where $p$…

Given a prime power $p^d$ with $p$ a prime and $d$ a positive integer, we classify the finite groups $G$ with $p^{2d}$ dividing $|G|$ in which all subgroups of order $p^d$ are complemented and the finite groups $G$ having a normal…

We make further progress towards a Kneser-type generalization of Pollard's Theorem to general abelian groups. For two sets $A$ and $B$ in an abelian group $G$, the \emph{$t$-popular sumset} of $A$ and $B$, denoted by $A+_t B$, is the set of…

We prove that for every compactum $X$ and every integer $n \geq 2$ there are a compactum $Z$ of $\dim \leq n+1$ and a surjective $UV^{n-1}$-map $r: Z \lo X$ such that for every abelian group $G$ and every integer $k \geq 2$ such that…

Let $S(a,b)$ denote the normalized Dedekind sum. We study the range of possible values for $S(a,b)=\frac{k}{q}$ with $\gcd(k,q)=1$. Girstmair proved local restrictions on $k$ depending on $q\pmod{12}$ and whether $q$ is a square and…

We present a multi-parameter non-constant-invariant class of Abel ordinary differential equations with the following remarkable features. This one class is shown to unify, that is, contain as particular cases, all the integrable classes…

Let $G$ be a multiplicative subsemigroup of the general linear group $\Gl(\mathbb{R}^d)$ which consists of matrices with positive entries such that every column and every row contains a strictly positive element. Given a $G$--valued random…

We study group extensions of Finite Abelian Groups using matrices. We also prove a Theorem for equivalence of extensions using matrices.

We formulate generalizations of Pauli's theorem on the cases of real and complex Clifford algebras of even and odd dimensions. We give analogues of these theorems in matrix formalism. Using these theorems we present an algorithm for…

Crystalline graded rings are generalizations of certain classes of rings like generalized twisted group rings, generalized Weyl algebras, and generalized skew crossed products. When the base ring is a commutative Dedekind domain, two…

We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in the ordinary case. In the modular case, we propose a…