Related papers: Generators of Picard modular groups

Irrespective of whether n is prime, prime power with exponent >1, or composite, the group U_n of units of Z_n can sometimes be obtained as the direct product of cyclic groups generated by x, x+k and x+2k, for x, k in Z_n. Indeed, for many…

We use polyhedral product models to analyse the structure of the commutator subgroup of a right-angled Artin group. In particular, we provide a minimal set of generators for the commutator subgroup, consisting of special iterated…

We study the Gram matrix determinants for the groups $S_n,O_n,B_n,H_n$, for their free versions $S_n^+,O_n^+,B_n^+,H_n^+$, and for the half-liberated versions $O_n^*,H_n^*$. We first collect all the known computations of such determinants,…

In this work, we derive the low index subgroups of the extended Hecke, Hecke and the Picard groups using tools in color symmetry theory. We also present the low index subgroups of the modular group.

The regular subgroup determining an induced Hopf Galois structure for a Galois extension $L/K$ is obtained as the direct product of the corresponding regular groups of the inducing subextensions. We describe here the associated Hopf algebra…

We describe a procedure for generating families of cyclic cubic fields with explicit fundamental units. This method generates all known families and gives new ones.

We determine the rational divisor class group of the moduli spaces of smooth pointed hyperelliptic curves and of their Deligne-Mumford compactification, over the field of complex numbers.

We give a conjectural presentation of the infinitely generated group PGL(2,Q) with an infinite list of relators.

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 exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation a fundamental domain and linear algebra.

We calculate the group $\kappa_2$ of exotic elements in the $K(2)$-local Picard group at the prime $2$ and find it is a group of order $2^9$ isomorphic to $(\mathbb{Z}/8)^2 \times (\mathbb{Z}/2)^3$. In order to do this we must define and…

We show that the subgroup of the Picard group of a $p$-block of a finite group given by bimodules with endopermutation sources modulo the automorphism group of a source algebra is determined locally in terms of the fusion system on a defect…

We show that the Picard group $Pic(A(1))$ of the stable category of modules over $\mathbb{C}$-motivic $A(1)$ is isomorphic to $\mathbb{Z}^4$. By comparison, the Picard group of classical $A(1)$ is $\mathbb{Z}^2 \oplus \mathbb{Z}/2$. One…

We investigate the periodic structure of the exponential pseudorandom number generator obtained from the map $x\mapsto g^x\pmod p$ that acts on the set $\{1, \ldots, p-1\}$.

We analyze the stable isomorphism type of polynomial rings on degree 1 generators as modules over the sub-algebra A(1) = <Sq^1, Sq^2> of the mod 2 Steenrod algebra. Since their augmentation ideals are Q_1-local, we do this by studying the…

We propose a class of generating functions denoted by $\textrm{RGF}_p(x)$, which is related to the Sylvester denumerant for the quotients of numerical semigroups. Using MacMahon's partition analysis, we can obtain $\textrm{RGF}_p(x)$ by…

Let $L$ be a proper finite extension of the field of $p$-adic numbers and let $o\subset L$ be its integers, viewed as an abelian locally $L$-analytic group. Let $\hat{o}$ be the rigid analytic group variety parametrizing the locally…

We develop pivotal and spherical versions of graded extension theory. We define the corresponding analogues of Brauer-Picard $2$-categorical groups and realize them as fixed points of natural $\mathbb{Z}$ and $\mathbb{Z}/2\mathbb{Z}$…

From [Problem 1729, Groups of prime power order, Vol. 3], Berkovich et al. asked to obtain the Schur multiplier and the representation of a group $G$, when $G$ is a special $p$-group minimally generated by $d$ elements and…

Generating functions for Clebsch-Gordan coefficients of osp(1|2) are derived. These coefficients are expressed as q goes to - 1 limits of the dual q-Hahn polynomials. The generating functions are obtained using two different approaches…