Related papers: On computing finite index subgroups of PSL(2,Z)

The theory of subfactors of groups, together with the associated notions of subindices and index stability for groupsandtheirsubsets, hasrecentlybeenintroducedandsystematicallydeveloped. Theseconceptsexhibitdeepconnections with additive…

Let $\mathfrak{o}$ be a compact discrete valuation ring and $n\geq 2$. We introduce a method to study the cotype zeta function of subalgebras of $\mathfrak{o}^n$. This multivariable series encodes the number of finite-index subalgebras…

Let $F$ be any field. We give a short and elementary proof that any finite subgroup $G$ of $PGL(2,F)$ occurs as a Galois group over the function field $F(x)$. We also develop a theory of descent to subfields of $F$. This enables us to…

We enumerate the number of isoclinism classes of semi-extraspecial $p$-groups with derived subgroup of order $p^2$. To do this, we enumerate $\text{GL}(2, p)$-orbits of sets of irreducible, monic polynomials in $\mathbb{F}_p[x]$. Along the…

For convex co-compact subgroups of SL2(Z) we consider the "congruence subgroups" for p prime. We prove a factorization formula for the Selberg zeta function in term of L-functions related to irreducible representations of the Galois group…

The method of subquotients is developed and used to determine all finite dimensional rank 2 Nichols algebras of diagonal type over an arbitrary field of characteristic zero. Key Words: Hopf algebra, Nichols algebra

We develop a practical method for computing local zeta functions of groups, algebras, and modules in fortunate cases. Using our method, we obtain a complete classification of generic local representation zeta functions associated with…

This paper deals with the number of subgroups of a given exponent in a finite abelian group. Explicit formulas are obtained in the case of rank two and rank three abelian groups. An asymptotic formula is also presented.

In this paper we study ends of finitely generated semigroups. The ends we are working with are the ends of the undirected graphs of Cayley graphs of finitely generated semigroups. We prove that the number of ends is preserved for…

We study that over some types of trees with a given number of vertices, which trees minimize or maximize the total number of subtrees. Trees minimizing (resp. maximizing) the total number of subtrees usually maximize (resp. minimize) the…

We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi$ or $\log(2)$. In order to perform these simplifications, we view the series as specializations of…

We examine the behavior of the sequences of $p$-adic valuations of quadratic polynomials with integer coefficients for an odd prime $p$ through tree representations. Under this representation, a finite tree corresponds to a periodic…

The Lewis Correspondence attaching a unique "period function" to each Maass wave form for SL(2,Z) is extended to subgroups of finite index. This is achieved by using vector-valued forms.

We compute Euler characteristics of p-subgroup categories of finite groups

We give an algorithm to determine finitely many generators for a subgroup of finite index in the unit group of an integral group ring $\mathbb{Z} G$ of a finite nilpotent group $G$, this provided the rational group algebra $\mathbb{Q} G$…

We use the theory of \Gamma-species to enumerate k-gonal and polygonal 2-trees with respect to their vertices. We then extend this result to enumerate "succulents", a tree-like class of graphs which generalize cacti.

To a tree of semi-simple algebras we associate a qurve (or formally smooth algebra) S. We introduce a Zariski- and etale quiver describing the finite dimensional representations of S. In particular, we show that all quotient varieties of…

In this paper, we present a novel approach for calculating the set of subgroups of a finite group, focusing on cyclic subgroups, and using it to establish the quantity of all subgroups in the direct product of two groups. Specifically, we…

Arithmetic Kleinian groups are arithmetic lattices in PSL_2(C). We present an algorithm which, given such a group Gamma, returns a fundamental domain and a finite presentation for Gamma with a computable isomorphism.

We study a geometric construction of certain finite index subgroups of Aut(F2).