Let G be a group and D be a subgroup of G. In this paper we are interested in the description of the lattice L(D; G) = fH j D H Gg of subgroups of G which contain D. We call subgroups H 2 L(D; G) subgroups intermediate between D and G. We are primarily interested in the parametrization of intermediate subgroups and their behaviour with respect to set-theoretic and group-theoretic operations lik...

We prove that there exists an integer p0 such that X split (p)(Q) is made of cusps and CM-points for any prime p > p0. Equivalently, for any non-CM elliptic curve E over Q and any prime p > p0 the image of the representation of Gal(¯ Q/Q) induced by the Galois action on the p-division points of E is not contained in the normalizer of a split Cartan subgroup. This gives a partial answer to an ol...

Many logical systems justify their consistency via proofs of cut elimination or normalization. However, these metatheoretic proofs inevitably use a transfinite induction which cannot be proved wellfounded within the system itself. We present evident logic, a logical system with a normalization proof which does not require any induction that is stronger than what is available within the logical ...

A composite quantum system comprising a finite number k of subsystems which are described with position and momentum variables in Zni , i = 1, . . . , k, is considered. Its Hilbert space is given by a k-fold tensor product of Hilbert spaces of dimensions n1, . . . , nk. Symmetry group of the respective finite Heisenberg group is given by the quotient group of certain normalizer. This paper exte...

For any set X and any relation on X, let T (X, ) be the semigroup of all maps a : X → X that preserve . Let S(X) be the symmetric group on X. If is reflexive, the group of automorphisms of T (X, ) is isomorphic toNS(X)(T (X, )), the normalizer of T (X, ) in S(X), that is, the group of permutations on X that preserve T (X, ) under conjugation. The elements ofNS(X)(T (X, )) have been described fo...

In this study, the problem of shallow parsing of Hindi-English code-mixed social media text (CSMT) has been addressed. We have annotated the data, developed a language identifier, a normalizer, a part-of-speech tagger and a shallow parser. To the best of our knowledge, we are the first to attempt shallow parsing on CSMT. The pipeline developed has been made available to the research community w...

Python implementation of permutations is presented. Three classes are introduced: Perm for permutations, Group for permutation groups, and PermError to report any errors for both classes. The class Perm is based on Python dictionaries and utilize cycle notation. The methods of calculation for the perm order, parity, ranking and unranking are given. A random permutation generation is also shown....

Let $\Gamma_n(\mathcal{\scriptstyle{O}}_\mathbb{K})$ denote the Hermitian modular group of degree $n$ over an imaginary-quadratic number field $\mathbb{K}$. In this paper we determine its maximal discrete extension in $SU(n,n;\mathbb{C})$, which coincides with normalizer $\Gamma_n(\mathcal{\scriptstyle{O}}_{\mathbb{K}})$. The description involves $n$-torsion subgroup ideal class This is defined...

Consider a compact locally symmetric space M of rank r, with fundamental group Γ. The von Neumann algebra VN(Γ) is the convolution algebra of functions f ∈ l2(Γ) which act by left convolution on l2(Γ). Let T r be a totally geodesic flat torus of dimension r in M and let Γ0 ∼= Z r be the image of the fundamental group of T r in Γ. Then VN(Γ0) is a maximal abelian ⋆-subalgebra of VN(Γ) and its un...