New Symmetric (61,16,4) Designs Invariant Under the Dihedral Group of Order 10

∗ This work has been partially supported by the Bulgarian NSF under Contract No. I-506/1995.

Structure of the Unit Group of FD10

2000 Mathematics Subject Classification: 16U60, 20C05.

EXTENSION OF AUTOMORPHISMS OF SUBGROUPS

Let G be a group such that, for any subgroup H of G, every automorphism of H can be extended to an automorphism of G. Such a group G is said to be of injective type. The finite abelian groups of injective type are precisely the quasi-injective groups. We prove that a finite non-abelian group G of injective type has even order. If, furthermore, G is also quasi-injective, then we prove that G = K x B, with B a quasi-injective abelian group of odd order and either K = Q(8) (the quaternion group of order 8) or K = Dih(A), a dihedral group on a quasi-injective abelian group A of odd order coprime with the order of B. We give a description of the supersoluble finite groups of injective type whose Sylow 2-subgroup are abelian showing that these groups are, in general, not quasi-injective. In particular, the characterisation of such groups is reduced to that of finite 2-groups that are of injective type. We give several restrictions on the latter. We also show that the alternating group A(5) is of injective type but that the binary icosahedral group SL(2, 5) is not.

On realizability of p-groups as Galois groups

2000 Mathematics Subject Classification: 12F12, 15A66.

The D(D-3)-anyon chain: integrable boundary conditions and excitation spectra

Chains of interacting non-Abelian anyons with local interactions invariant under the action of the Drinfeld double of the dihedral group D-3 are constructed. Formulated as a spin chain the Hamiltonians are generated from commuting transfer matrices of an integrable vertex model for periodic and braided as well as open boundaries. A different anyonic model with the same local Hamiltonian is obtained within the fusion path formulation. This model is shown to be related to an integrable fusion interaction round the face model. Bulk and surface properties of the anyon chain are computed from the Bethe equations for the spin chain. The low-energy effective theories and operator content of the models (in both the spin chain and fusion path formulation) are identified from analytical and numerical studies of the finite-size spectra. For all boundary conditions considered the continuum theory is found to be a product of two conformal field theories. Depending on the coupling constants the factors can be a Z(4) parafermion or a M-(5,M-6) minimal model.

Azo-group dihedral angle torsion dependence on temperature: A theorerical-experimental study

Quantum chemical calculations were carried out to explain the observed shifts in the absorption spectrum of different azo-aromatic compounds due to changes in the dihedral angle of the azo-group. Our results reveal that the pi-pi* transition presents a hypsochromic shift and an oscillator strength drop upon increase of the dihedral angle. Nevertheless, the pi-pi* transition exhibits the opposite behavior. This effect is attributed to the reduction in the pi-electron conjugation length of the molecule. Experimentally, we performed temperature dependence measurements of the linear absorption spectrum. Both the theoretical and experimental results demonstrate that small energy changes are mirrored in the electronic transitions of conjugated linear molecules. (C) 2010 Elsevier B.V. All rights reserved.