Search results for "Groups"

Some applications of a fundamental theorem by Gluck and Wolf in the character theory of finite groups

1986

On the representation theory of quantum Heisenberg group and algebra

1994

We show that the quantum Heisenberg groupH q (1) and its *-Hopf algebra structure can be obtained by means of contraction from quantumSU q (2) group. Its dual Hopf algebra is the quantum Heisenberg algebraU q (h(1)). We derive left and right regular representations forU q (h(1)) as acting on its dualH q (1). Imposing conditions on the right representation, the left representation is reduced to an irreducible holomorphic representation with an associated quantum coherent state. Realized in the Bargmann-Hilbert space of analytic functions the unitarity of regular representation is also shown. By duality, left and right regular representations for quantum Heisenberg group with the quantum Heis…

Nilpotent and abelian Hall subgroups in finite groups

2015

[EN] We give a characterization of the finite groups having nilpotent or abelian Hall pi-subgroups that can easily be verified using the character table.

Characters and Blocks of Finite Groups

1998

This is a clear, accessible and up-to-date exposition of modular representation theory of finite groups from a character-theoretic viewpoint. After a short review of the necessary background material, the early chapters introduce Brauer characters and blocks and develop their basic properties. The next three chapters study and prove Brauer's first, second and third main theorems in turn. These results are then applied to prove a major application of finite groups, the Glauberman Z*-theorem. Later chapters examine Brauer characters in more detail. The relationship between blocks and normal subgroups is also explored and the modular characters and blocks in p-solvable groups are discussed. Fi…

Groups with exactly one irreducible character of degree divisible byp

2014

Let [math] be a prime. We characterize those finite groups which have precisely one irreducible character of degree divisible by [math] .

ON AUTOMORPHISMS OF GENERALIZED ALGEBRAIC-GEOMETRY CODES.

2007

Abstract We consider a class of generalized algebraic-geometry codes based on places of the same degree of a fixed algebraic function field over a finite field F / F q . We study automorphisms of such codes which are associated with automorphisms of F / F q .

Algebraic Groups and Lie Groups with Few Factors

2008

In the theory of locally compact topological groups, the aspects and notions from abstract group theory have conquered a meaningful place from the beginning (see New Bibliography in [44] and, e.g. [41–43]). Imposing grouptheoretical conditions on the closed connected subgroups of a topological group has always been the way to develop the theory of locally compact groups along the lines of the theory of abstract groups. Despite the fact that the class of algebraic groups has become a classical object in the mathematics of the last decades, most of the attention was concentrated on reductive algebraic groups. For an affine connected solvable algebraic group G, the theorem of Lie–Kolchin has b…

Quantitative Vibrational Spectrometry in the 21st Century: A Scientometric Evaluation

2005

Abstract The state of the art of research on vibrational spectrometry–based quantitative methodologies was evaluated from the literature compiled in Analytical Abstracts from 1980. Medium and near infrared, Raman spectrometry, and photoacoustic methods of analysis were considered. The evolution of the number of published papers, the distribution of the literature as a function of the different application fields in which the vibrational methods were employed, and a study of the impact on this area of chemometric and automation studies clearly shows that, from the 1990s until now, the importance of vibrational spectrometry in application analysis has grown to reach maturity. This field provi…

Developmental trends in children's pretend play.

1991

The developmental trends in pretend play were investigated in children 2-6 years of age (18 in each of five age groups) by examining changes in pretend action and speech separately. Play behaviour was assessed by using a selected set of Duplo Lego toys. Interest focused on occurrence of decentration, decontextualization and integration at different age levels. The proportions of decentred and decontextualized acts, action integrations and play themes, increased linearly with age. Changes in substitutive and inventive actions were, however, more minor than expected. Single-scheme combinations did not reveal any essential aspect of the development of children's symbolic competence. In this se…

Symmetry and models of single-walled TiO2 nanotubes with rectangular morphology

2011

Abstract The formalism of line symmetry groups for one-periodic (1D) nanostructures with rotohelical symmetry has been applied for symmetry analysis of single-walled titania nanotubes (SW TiO2 NTs) formed by rolling up the stoichiometric two-periodic (2D) slabs of anatase structure. Either six- or twelve-layer (101) slabs have been cut from TiO2 crystal in a stable anatase phase. After structural optimization, the latter keeps the centered rectangular symmetry of initial slab slightly compressed along a direction coincided with large sides of elemental rectangles. We have considered two sets of SW TiO2 NTs with optimized six- and twelve-layer structures, which possess chiralities (−n, n) an…