Related papers: Modular unit and cuspidal divisor class groups of …

In this paper we give an explicit formula for the number of subgroups of the modular group of a given index that are genus zero and torsion-free and a formula for their conjugacy classes. We do so by exhibiting a correspondence between…

Let $M$ and $N$ be positive integers for which the modular curve $X_1(M,MN)$ has genus $0$, and let $p$ be a prime divisor of $MN$. This article gives asymptotic lower bounds for the average size of the $p$-Selmer group of elliptic curves…

We establish an Excision type theorem for niceness of group structure on the orbit space of unimodular rows of length $n$ modulo elementary action. This permits us to establish niceness for relative versions of results for the cases when $n…

The aim of this paper is to introduce and to investigate the analogues of torsors for compact quantum groups and to study their role in representation theory. Let A be a unitarizable Hopf *-algebra: we show that there is a category…

Let $N$ and $H$ be groups, and let $G$ be an extension of $H$ by $N$. In this article we describe the structure of the complex group ring of $G$ in terms of data associated with $N$ and $H$. In particular, we present conditions on the…

We consider the action of $p$-toral subgroups of $U(n)$ on the unitary partition complex $\mathcal L_n$. We show that if $H\subseteq U(n)$ is $p$-toral and has noncontractible fixed points on $\mathcal L_n$, then the image of $H$ in the…

We give a decomposition of the equivariant Kasparov category for discrete quantum group with torsions. As an outcome, we show that the crossed product by a discrete quantum group in a certain class preserves the UCT. We then show that…

Let $C$ be an additive category with cokernels and let Mod($C$) be the category of additive functors from $C^{op}$ to the category Ab of abelian groups. Let mod($C$) be the full subcategory of Mod($C$) consisting of coherent functors. In…

Let $E$ be an elliptic curve, defined over a quartic extension $K$ of $\mathbb{Q}$, with $j(E) \in \mathbb{Q}$. In this paper, we classify the possible torsion subgroup structures $E(K)_{\text{tors}}$.

Let $p$ be a prime integer and $n,i$ be positive integers such that \linebreak $S=\{-1, \ \theta, \ \mu_i=1+\theta+... + \theta^{i-1} \ \mid 1 < i < \frac{p^n}{2}, \ gcd(p^n,i)=1 \}$ generates the group of units of $\mathbb{Z}[\theta],$…

Serre proved that any holomorphic cusp form of weight one for $\Gamma_1(N)$ is lacunary while a holomorphic modular form for $\Gamma_1(N)$ of higher integer weight is lacunary if and only if it is a linear combination of cusp forms of…

Hans Zassenhaus conjectured that every torsion unit of the integral group ring of a finite group $G$ is conjugate within the rational group algebra to an element of the form $\pm g$ with $g\in G$. This conjecture has been disproved recently…

H.J. Zassenhaus conjectured that any unit of finite order and augmentation $1$ in the integral group ring $\mathbb{Z}G$ of a finite group $G$ is conjugate in the rational group algebra $\mathbb{Q}G$ to an element of $G$. We prove the…

In the classification theorems of Vinberg and Yakimova for commutative nilmanifolds, the relevant nilpotent groups have a very surprising analytic property. The manifolds are of the form $G/K = N \rtimes K/K$ where, in all but three cases,…

In this paper, the module algebra structures of $X_{q}(A_{1})$ on quantum polynomial algebra $\C_{q}[x,y,z]$ are investigated, and a complete classification of $X_{q}(A_{1})$-module algebra structures on $\C_{q}[x,y,z]$ is given

It is proved that for any prime $p$ a finitely generated nilpotent group is conjugacy separable in the class of finite $p$-groups if and only if the torsion subgroup of it is a finite $p$-group and the quotient group by the torsion subgroup…

The semigroups of unital extensions of separable $C^\ast$-algebras come in two flavours: a strong and a weak version. By the unital $\mathrm{Ext}$-groups, we mean the groups of invertible elements in these semigroups. We use the unital…

We introduce a new invariant for C*-algebras of stable rank one that merges the Cuntz semigroup information together with the K$_1$-group information. This semigroup, termed the Cu$_1$-semigroup, is constructed as equivalence classes of…

We give a function F(d,n,p) such that if K/Q_p is a degree n field extension and A/K is a d-dimensional abelian variety with potentially good reduction, then #A(K)[tors] is at most F(d,n,p). Separate attention is given to the prime-to-p…

A pseudomodular group is a discrete subgroup $\Gamma \leq PGL(2,\mathbb{Q})$ which is not commensurable with $PSL(2,\mathbb{Z})$ and has cusp set precisely $\mathbb{Q}\cup\{\infty\}$. The existence of such groups was proved by Long and…