PROJECTIVE CHARACTERS WITH PRIME POWER DEGREES

2018 ◽  
Vol 99 (1) ◽  
pp. 78-82
Author(s):  
YANG LIU
Keyword(s):  
Structural Information ◽  
Character Degrees ◽  
Character Theory ◽  
Induced Representations ◽  
Projective Character ◽  
Projective Representations ◽  
A Finite Group ◽  
The Relationship ◽  
Factor Set ◽  
Representation Group

We consider the relationship between structural information of a finite group $G$ and $\text{cd}_{\unicode[STIX]{x1D6FC}}(G)$, the set of all irreducible projective character degrees of $G$ with factor set $\unicode[STIX]{x1D6FC}$. We show that for nontrivial $\unicode[STIX]{x1D6FC}$, if all numbers in $\text{cd}_{\unicode[STIX]{x1D6FC}}(G)$ are prime powers, then $G$ is solvable. Our result is proved by classical character theory using the bijection between irreducible projective representations and irreducible constituents of induced representations in its representation group.

scholarly journals Groups whose Projective character degrees are powers of a prime

1988 ◽  
Vol 30 (2) ◽  
pp. 177-180 ◽  
Author(s):  
R. J. Higgs
Keyword(s):  
Finite Group ◽  
Projective Representation ◽  
Character Degrees ◽  
Projective Character ◽  
Projective Representations ◽  
A Finite Group

Let Gbe a finite group, and P:G → GL(n, ) be such that for all x, y ∈ G(i) P(x)P(y) = α(x, y)P(xy), and(ii)P(l) = In,where α(x, y) ∈ *; then P is a projective representation of G with cocycle α and degree n. For other basic definitions concerning projective representations see [4].

THE BAD BEHAVIOR OF REPRESENTATION GROUPS

2005 ◽  
Vol 04 (02) ◽  
pp. 139-151
Author(s):  
R. J. HIGGS
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Central Extension ◽  
Full Automorphism Group ◽  
Character Tables ◽  
Projective Character ◽  
Inner Automorphisms ◽  
A Finite Group ◽  
Representation Group

Let (H, A) be a primitive central extension of a finite group G. We show that A is not characteristic in H in general, and further demonstrate in a series of examples that results, which hold about inner automorphisms of H, do not extend to the full automorphism group of H. We also give some new results about isoclinism and representation groups of G in the case that H is capable. Finally we give an example of two non-isomorphic groups of the same order, which not only have a representation group in common, but also have identical projective character tables.

scholarly journals Phenotyping plants: genes, phenes and machines

2012 ◽  
Vol 39 (11) ◽  
pp. 813 ◽  
Author(s):  
Roland Pieruschka ◽  
Hendrik Poorter
Keyword(s):  
Structural Information ◽  
Plant Phenotyping ◽  
Phenotypic Traits ◽  
Special Issue ◽  
Non Invasive ◽  
The Core ◽  
The Relationship ◽  
Non Destructive ◽  
Major Progress ◽  
Meaningful Data

No matter how fascinating the discoveries in the field of molecular biology are, in the end it is the phenotype that matters. In this paper we pay attention to various aspects of plant phenotyping. The challenges to unravel the relationship between genotype and phenotype are discussed, as well as the case where ‘plants do not have a phenotype’. More emphasis has to be placed on automation to match the increased output in the molecular sciences with analysis of relevant traits under laboratory, greenhouse and field conditions. Currently, non-destructive measurements with cameras are becoming widely used to assess plant structural properties, but a wider range of non-invasive approaches and evaluation tools has to be developed to combine physiologically meaningful data with structural information of plants. Another field requiring major progress is the handling and processing of data. A better e-infrastructure will enable easier establishment of links between phenotypic traits and genetic data. In the final part of this paper we briefly introduce the range of contributions that form the core of a special issue of this journal on plant phenotyping.

scholarly journals Anharmonicity and Spectra–Structure Correlations in MIR and NIR Spectra of Crystalline Menadione (Vitamin K3)

Molecules ◽  
2021 ◽  
Vol 26 (22) ◽  
pp. 6779
Author(s):  
Krzysztof B. Beć ◽  
Justyna Grabska ◽  
Christian W. Huck ◽  
Sylwester Mazurek ◽  
Mirosław A. Czarnecki
Keyword(s):  
Single Molecule ◽  
Near Infrared ◽  
Structural Information ◽  
Molecular System ◽  
Theoretical Calculations ◽  
Vitamin K3 ◽  
Structure Correlations ◽  
Mir Spectra ◽  
Combination Bands ◽  
The Relationship

Mid-infrared (MIR) and near-infrared (NIR) spectra of crystalline menadione (vitamin K3) were measured and analyzed with aid of quantum chemical calculations. The calculations were carried out using the harmonic approach for the periodic model of crystal lattice and the anharmonic DVPT2 calculations applied for the single molecule model. The theoretical spectra accurately reconstructed the experimental ones permitting for reliable assignment of the MIR and NIR bands. For the first time, a detailed analysis of the NIR spectrum of a molecular system based on a naphthoquinone moiety was performed to elucidate the relationship between the chemical structure of menadione and the origin of the overtones and combination bands. In addition, the importance of these bands during interpretation of the MIR spectrum was demonstrated. The overtones and combination bands contribute to 46.4% of the total intensity of menadione in the range of 3600–2600 cm−1. Evidently, these bands play a key role in shaping of the C-H stretching region of MIR spectrum. We have shown also that the spectral regions without fundamentals may provide valuable structural information. For example, the theoretical calculations reliably reconstructed numerous overtones and combination bands in the 4000–3600 and 2800–1800 cm−1 ranges. These results, provide a comprehensive origin of the fundamentals, overtones and combination bands in the NIR and MIR spectra of menadione, and the relationship of these spectral features with the molecular structure.

scholarly journals CYTOGENETIC ANALYSIS OF THE CHROMOSOMAL REGION IMMEDIATELY ADJACENT TO THE ROSY LOCUS IN DROSOPHILA MELANOGASTER

Genetics ◽  
1980 ◽  
Vol 95 (1) ◽  
pp. 95-110 ◽  
Author(s):  
Arthur J Hilliker ◽  
Stephen H Clark ◽  
Arthur Chovnick ◽  
William M Gelbart
Keyword(s):  
Drosophila Melanogaster ◽  
Polytene Chromosome ◽  
Structural Information ◽  
Genetic Regulation ◽  
Chromosome Band ◽  
Genetic Dissection ◽  
Genetic Unit ◽  
Complementation Groups ◽  
The Relationship ◽  
Chromosome Bands

ABSTRACT This report describes the genetic analysis of a region of the third chromosome of Drosophila melanogaster extending from 87D2-4 to 87E12-F1, an interval of 23 or 24 polytene chromosome bands. This region includes the rosy (ry, 3-52.0) locus, carrying the structural information for xanthine dehydrogenase (XDH). We have, in recent years, focused attention on the genetic regulation of the rosy locus and, therefore, wished to ascertain in detail the immediate genetic environmcnt of this locus. Specifically, we question if rosy is a solitary genetic unit or part of a larger complex genetic unit encompassing adjacent genes. Our data also provide opportunity to examine further the relationship between euchromatic gene distrihution and polytene chromosome structure.—The results of our genetic dissection of the rosy microregion substantiate the conclusion drawn earlier (SCHALET, KERNAGHAN and CHOVNICK 1964) that the rosy locus is the only gene in this region concerned with XDH activity and that all adjacent genetic units are functionally, as well as spatially, distinct Erom the rosy gene. Within the rosy micro-region, we observed a close correspondence between the number of complementation groups (21) and the number of polytene chromosome bands (23 or 24). Consideration of this latter observation in conjunction with those of similar studies of other chhromosomal regions supports the hypothesis that each polytene chromosome band corresponds to a single genetic unit.

scholarly journals Epistatic contributions promote the unification of incompatible models of neutral molecular evolution

2020 ◽  
Vol 117 (11) ◽  
pp. 5873-5882 ◽  
Author(s):  
Jose Alberto de la Paz ◽  
Charisse M. Nartey ◽  
Monisha Yuvaraj ◽  
Faruck Morcos
Keyword(s):  
Structural Information ◽  
Stokes Shift ◽  
Neutral Evolution ◽  
Emergent Properties ◽  
Sequence Evolution ◽  
Sequence Alignments ◽  
Multiple Sequence ◽  
Multiple Sequence Alignments ◽  
Analysis Methodology ◽  
The Relationship

We introduce a model of amino acid sequence evolution that accounts for the statistical behavior of real sequences induced by epistatic interactions. We base the model dynamics on parameters derived from multiple sequence alignments analyzed by using direct coupling analysis methodology. Known statistical properties such as overdispersion, heterotachy, and gamma-distributed rate-across-sites are shown to be emergent properties of this model while being consistent with neutral evolution theory, thereby unifying observations from previously disjointed evolutionary models of sequences. The relationship between site restriction and heterotachy is characterized by tracking the effective alphabet dynamics of sites. We also observe an evolutionary Stokes shift in the fitness of sequences that have undergone evolution under our simulation. By analyzing the structural information of some proteins, we corroborate that the strongest Stokes shifts derive from sites that physically interact in networks near biochemically important regions. Perspectives on the implementation of our model in the context of the molecular clock are discussed.

The finite inner automorphism groups of division rings

1995 ◽  
Vol 118 (2) ◽  
pp. 207-213 ◽  
Author(s):  
M. Shirvani
Keyword(s):  
Finite Groups ◽  
Galois Theory ◽  
Automorphism Groups ◽  
Outer Automorphism ◽  
Commutative Field ◽  
Division Rings ◽  
Inner Automorphism ◽  
Projective Representations ◽  
Inner Automorphisms ◽  
A Finite Group

Let G be a finite group of automorphisms of an associative ring R. Then the inner automorphisms (x↦ u−1xu = xu, for some unit u of R) contained in G form a normal subgroup G0 of G. In general, the Galois theory associated with the outer automorphism group G/G0 is quit well behaved (e.g. [7], 2·3–2·7, 2·10), while little group-theoretic restriction on the structure of G/G0 may be expected (even when R is a commutative field). The structure of the inner automorphism groups G0 does not seem to have received much attention so far. Here we classify the finite groups of inner automorphisms of division rings, i.e. the finite subgroups of PGL (1, D), where D is a division ring. Such groups also arise in the study of finite collineation groups of projective spaces (via the fundamental theorem of projective geometry, cf. [1], 2·26), and provide examples of finite groups having faithful irreducible projective representations over fields.

scholarly journals Antioxidant Activity of Metabolites from Coleonema Album (Rutaceae)

2006 ◽  
Vol 1 (5) ◽  
pp. 1934578X0600100 ◽  
Author(s):  
Lindy L. Esterhuizen ◽  
Riaan Meyer ◽  
Ian A. Dubery
Keyword(s):  
Antioxidant Activity ◽  
South African ◽  
Structural Information ◽  
Radical Scavenging Activity ◽  
Radical Scavenging ◽  
Reducing Power ◽  
Active Components ◽  
Bioassay Guided Fractionation ◽  
The Relationship

Coleonema album, a member of the South African ‘Fynbos’ biome, was evaluated for its antioxidant and free radical scavenging activity. Ethanol- and acetone-based extracts from plant material obtained from two different geographical areas were analysed. A bioassay-guided fractionation methodology was followed for screening of active compounds. The 1,1-diphenyl-2-picrylhydrazyl (DPPH)-TLC method revealed the presence of a number of antioxidants which were quantified by the DPPH-spectrophotometric assay and the oxygen radical absorbance capacity (ORAC) assay. The C. album extracts possessed significant in vitro antioxidant activity, a large portion of which appeared to be contributed by the phenolic compounds. In contrast, the reducing power of the extracts could not be correlated with the observed antioxidant activity. Identification and structural information of the active components were obtained by a combination of preparative TLC and LC-MS which revealed the presence of coumarin aglycones and glycosides. The results of this study indicate that C. album contains strong antioxidants that warrant further investigation into the relationship between the structure and activity of the active coumarin metabolites.

scholarly journals Word problems for finite nilpotent groups

2020 ◽  
Vol 115 (6) ◽  
pp. 599-609
Author(s):  
Rachel D. Camina ◽  
Ainhoa Iñiguez ◽  
Anitha Thillaisundaram
Keyword(s):  
Finite Group ◽  
Nilpotent Group ◽  
Finite Groups ◽  
Irreducible Character ◽  
Nilpotent Groups ◽  
Nilpotency Class ◽  
Character Degrees ◽  
Character Theory ◽  
Odd Order ◽  
Related Group

AbstractLet w be a word in k variables. For a finite nilpotent group G, a conjecture of Amit states that $$N_w(1)\ge |G|^{k-1}$$ N w ( 1 ) ≥ | G | k - 1 , where for $$g\in G$$ g ∈ G , the quantity $$N_w(g)$$ N w ( g ) is the number of k-tuples $$(g_1,\ldots ,g_k)\in G^{(k)}$$ ( g 1 , … , g k ) ∈ G ( k ) such that $$w(g_1,\ldots ,g_k)={g}$$ w ( g 1 , … , g k ) = g . Currently, this conjecture is known to be true for groups of nilpotency class 2. Here we consider a generalized version of Amit’s conjecture, which states that $$N_w(g)\ge |G|^{k-1}$$ N w ( g ) ≥ | G | k - 1 for g a w-value in G, and prove that $$N_w(g)\ge |G|^{k-2}$$ N w ( g ) ≥ | G | k - 2 for finite groups G of odd order and nilpotency class 2. If w is a word in two variables, we further show that the generalized Amit conjecture holds for finite groups G of nilpotency class 2. In addition, we use character theory techniques to confirm the generalized Amit conjecture for finite p-groups (p a prime) with two distinct irreducible character degrees and a particular family of words. Finally, we discuss the related group properties of being rational and chiral, and show that every finite group of nilpotency class 2 is rational.

scholarly journals On projective characters of prime degree

1991 ◽  
Vol 33 (3) ◽  
pp. 311-321 ◽  
Author(s):  
R. J. Higgs
Keyword(s):  
Prime Number ◽  
Structural Information ◽  
Alternating Group ◽  
Complex Numbers ◽  
Prime Degree ◽  
Counter Example ◽  
Projective Representations

All groups G considered in this paper are finite and all representations of G are defined over the field of complex numbers. The reader unfamiliar with projective representations is referred to [9] for basic definitions and elementary results.Let Proj(G, α) denote the set of irreducible projective characters of a group G with cocycle α. In a previous paper [3] the author showed that if G is a (p, α)-group, that is the degrees of the elements of Proj(G, α) are all powers of a prime number p, then G is solvable. However Isaacs and Passman in [8] were able to give structural information about a group G for which ξ(1) divides pe for all ξ ∈ Proj(G, 1), where 1 denotes the trivial cocycle of G, and indeed classified all such groups in the case e = l. Their results rely on the fact that G has a normal abelian p-complement, which is false in general if G is a (p, α)-group; the alternating group A4 providing an easy counter-example for p = 2.

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