Determination of Brauer Characters

1974 ◽  
Vol 26 (3) ◽  
pp. 746-752 ◽  
Author(s):  
B. M. Puttaswamaiah
Keyword(s):  
Group Algebra ◽  
Grothendieck Ring ◽  
Linear Character ◽  
Conjugate Class ◽  
Brauer Character ◽  
Integral Matrices ◽  
Brauer Characters ◽  
Characteristic Values ◽  
Category Of Modules

The purpose of this note is to show that the values of an irreducible (Brauer) character are the characteristic values of a matrix with non-negative rational integers. The construction of these integral matrices is done by a description of a representation of the Grothendieck ring of the category of modules over the group algebra. In particular a result of Solomon on characters and a result of Burnside on vanishing of a non-linear character on some conjugate class are generalized.

Brauer Characters and Grothendieck Rings

1975 ◽  
Vol 27 (5) ◽  
pp. 1025-1028 ◽  
Author(s):  
B. M. Puttaswamaiah
Keyword(s):  
Finite Order ◽  
Group Algebra ◽  
Irreducible Representations ◽  
Splitting Field ◽  
Finitely Generated ◽  
Grothendieck Ring ◽  
Primitive Idempotents ◽  
Brauer Characters ◽  
Grothendieck Rings ◽  
Special Case

Let G be a group of finite order g, A a splitting field of G of characteristic p (which may be 0) and R = AG the group algebra of G over A. In [2], the author studied some of the properties of the Grothendieck ring K(R) of the category of all finitely generated R-modules, and derived a number of consequences. This paper continues the study carried out in [2]. The study is concerned with the structure and irreducible representations of K(R). The ring K(R) is proved to be semisimple and the primitive idempotents of K(R) are explicitly constructed. If the ring K(R) is identified with the ‘algebra of representations', then Robinson's idempotent [3; 4; 5] follow from our description as a special case.

A Note on Brauer Character Degrees of Solvable Groups

1991 ◽  
Vol 34 (3) ◽  
pp. 423-425 ◽  
Author(s):  
You-Qiang Wang
Keyword(s):  
Solvable Group ◽  
Solvable Groups ◽  
Character Degrees ◽  
Finite Solvable Group ◽  
Prime Integer ◽  
Derived Length ◽  
Brauer Character ◽  
Brauer Characters

AbstractLet G be a finite solvable group. Fix a prime integer p and let t be the number of distinct degrees of irreducible Brauer characters of G with respect to the prime p. We obtain the bound 3t — 2 for the derived length of a Hall p'-subgroup of G. Furthermore, if |G| is odd, then the derived length of a Hall p'-subgroup of G is bounded by /.

scholarly journals Analysis of Methods for Determining Climate Loads at a Specified Territory Point by Meteorological Data

2020 ◽  
Vol 14 (2) ◽  
pp. 206-211
Author(s):  
Željko Kos ◽  
Viktor Pashynskyi ◽  
Yevhenii Klymenko ◽  
Mykola Pashynskyi
Keyword(s):  
Meteorological Data ◽  
Construction Materials ◽  
High Energy ◽  
Weather Data ◽  
Opposite Case ◽  
Relative Proximity ◽  
Characteristic Values ◽  
Building Standards ◽  
High Energy Consumption

Methods for determining the characteristic values of climate loads at the location of a building have been perfected. Based on comparative analysis, the method of levelling the values of climate loads with an exponential or triangular weight function is recommended. For four climate loads, appropriate equalization intervals are determined, ensuring the maximum amount of weather data taken into account, while maintaining their uniformity. In construction, the determination of the climate load is important for the location of the building. When prescribing building standards, the values of the climate load are determined according to the data of weather stations in relative proximity, which provides values within the limits of reliability. Such an approach can lead to an overestimation of the characteristic values of climate loads and consequently increase the consumption of the construction materials of the building or, in the opposite case, decrease the unnecessarily high-energy consumption to condition the space inside the building.

Mechanical properties of confirmat screws corner joints made of native wood and wood-based composites

2019 ◽  
Vol 105 ◽  
pp. 76-84
Author(s):  
NADEŽDA LANGOVÁ ◽  
PAVOL JOŠČÁK
Keyword(s):  
Mechanical Properties ◽  
Carrying Capacity ◽  
Limit State ◽  
Calculated Data ◽  
Statistical Processing ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Characteristic Values ◽  
State Method

Mechanical Properties of Confirmat Screws Corner Joints Made of Native Wood and Wood-Based Composites. The aim of this investigation was to design and determine the mechanical properties of confirmat screws corner joints made of native wood and wood-based composites. The objective of the study was to ascertain the stiffness and load carrying capacity of joints that differed in the diameter and length of confirmat type screw, as well as in the kind of materials. The results include statistical processing of measured and calculated data, and evaluation of the influence of selected factors on mechanical properties. The results are applied to the calculation of the characteristic values of the properties and to the determination of the equations for their calculation for other values of the selected factors. The characteristic values are used for the evaluation of the joints according to the limit state method.

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