On the Number of Cyclic Subgroups of Prime Order in the Group of Diagonal Matrices over a Circular Field

2020 ◽  
Vol 107 (3-4) ◽  
pp. 534-535
Author(s):  
U. M. Pachev ◽  
M. M. Isakova
Keyword(s):  
Prime Order ◽  
Cyclic Subgroups ◽  
Circular Field

scholarly journals On non-normal cyclic subgroups of prime order or order 4 of finite groups

2021 ◽  
Vol 19 (1) ◽  
pp. 63-68
Author(s):  
Pengfei Guo ◽  
Zhangjia Han
Keyword(s):  
Prime Order ◽  
Sufficient Conditions ◽  
Prime Power Order ◽  
Necessary And Sufficient Condition ◽  
Transitive Relation ◽  
Cyclic Subgroups ◽  
Formula Group ◽  
A Finite Group ◽  
Necessary And Sufficient

Abstract In this paper, we call a finite group G G an N L M NLM -group ( N C M NCM -group, respectively) if every non-normal cyclic subgroup of prime order or order 4 (prime power order, respectively) in G G is contained in a non-normal maximal subgroup of G G . Using the property of N L M NLM -groups and N C M NCM -groups, we give a new necessary and sufficient condition for G G to be a solvable T T -group (normality is a transitive relation), some sufficient conditions for G G to be supersolvable, and the classification of those groups whose all proper subgroups are N L M NLM -groups.

scholarly journals On the sandpile model of modified wheels II

2020 ◽  
Vol 18 (1) ◽  
pp. 1531-1539
Author(s):  
Zahid Raza ◽  
Mohammed M. M. Jaradat ◽  
Mohammed S. Bataineh ◽  
Faiz Ullah
Keyword(s):  
Direct Product ◽  
Critical Group ◽  
Complete Structure ◽  
Sandpile Model ◽  
Cyclic Subgroups ◽  
Algebr Comb ◽  
Abelian Sandpile ◽  
Chip Firing ◽  
Sandpile Group

Abstract We investigate the abelian sandpile group on modified wheels {\hat{W}}_{n} by using a variant of the dollar game as described in [N. L. Biggs, Chip-Firing and the critical group of a graph, J. Algebr. Comb. 9 (1999), 25–45]. The complete structure of the sandpile group on a class of graphs is given in this paper. In particular, it is shown that the sandpile group on {\hat{W}}_{n} is a direct product of two cyclic subgroups generated by some special configurations. More precisely, the sandpile group on {\hat{W}}_{n} is the direct product of two cyclic subgroups of order {a}_{n} and 3{a}_{n} for n even and of order {a}_{n} and 2{a}_{n} for n odd, respectively.

Functional encryption for computational hiding in prime order groups via pair encodings

2017 ◽  
Vol 86 (1) ◽  
pp. 97-120 ◽  
Author(s):  
Jongkil Kim ◽  
Willy Susilo ◽  
Fuchun Guo ◽  
Man Ho Au
Keyword(s):  
Prime Order ◽  
Functional Encryption

Optimisation of Magnification Levels for near Infrared Chemical Imaging of Blending of Pharmaceutical Powders

2007 ◽  
Vol 15 (3) ◽  
pp. 137-151 ◽  
Author(s):  
Hua Ma ◽  
Carl A. Anderson
Keyword(s):  
Near Infrared ◽  
Image Data ◽  
Principal Component ◽  
Chemical Imaging ◽  
Field Of View ◽  
Pharmaceutical Dosage Forms ◽  
Component Distribution ◽  
Circular Field ◽  
Pharmaceutical Powder ◽  
Magnification Level

A critical parameter in the evaluation of pharmaceutical dosage forms by hyperspectral imaging is the level of magnification. If the magnification (as set by the optical objective) is inadequate to resolve the relevant features, then the value of the imaging is diminished; if the magnification level is greater than is required, then the field of view is unnecessarily reduced. The purpose of this study was to determine an optimum magnification level for the study of powder mixing. Relevant features in this system include distribution of individual components within samples and the overall content of a given sample. In the present study, three magnification levels of near infrared (NIR) chemical imaging objectives were evaluated for their effects on imaging a blend of pharmaceutical materials (powders). High, medium and low objective magnification levels were investigated by comparing the resulting blend surface images of a two-component (salicylic acid and lactose) pharmaceutical powder mixture. Multiple images from high and medium magnification were concatenated so that an equivalent field of view was obtained for all magnification levels. Univariate images, principal component analysis score images, partial least squares predicted images and spectra extracted from different intensity regions in the area images were analysed qualitatively and quantitatively for comparison. A series of images spanning a strip across the centre of the circular field were collected at each magnification level and compared with respect to surface features elucidated and area of blend surface imaged. Analyses of images indicate that the three magnification levels delineate the component distribution for this particular powder system similarly. Images obtained at the low magnification level demonstrated adequate resolution and provided the broadest view of the blend surface. It is concluded that the low optical magnification level was adequate for the system being studied and is the preferred mode for pharmaceutical powder blend image data collection for this system.

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