A brief journey through extensions of rational groups

2018 ◽  
Vol 140 ◽  
pp. 123-128
Author(s):  
Stefan Friedenberg ◽  
Paul Wolf
Keyword(s):  
2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Temha Erkoç ◽  
Utku Yilmaztürk

AbstractA finite group whose irreducible complex characters are rational valued is called a rational group. Thus, G is a rational group if and only if N G(〈x〉)/C G(〈x〉) ≌ Aut(〈x〉) for every x ∈ G. For example, all symmetric groups and their Sylow 2-subgroups are rational groups. Structure of rational groups have been studied extensively, but the general classification of rational groups has not been able to be done up to now. In this paper, we show that a full symmetric group of prime degree does not have any rational transitive proper subgroup and that a rational doubly transitive permutation group containing a full cycle is the full symmetric group. We also obtain several results related to the study of rational groups.


2021 ◽  
Vol 5 (S1) ◽  
pp. 642-652
Author(s):  
Ahmad Zain Sarnoto ◽  
Lamya Hayatina

The purpose of this paper is to analyses the phenomenon of Muslims responding to government policies in overcoming the COVID-19 pandemic. This study is a review of the polarization of Muslims towards government policies to overcome the COVID-19 pandemic. There has been a change in the lifestyle of the Indonesian ‘Muslim community during the COVID-19 pandemic, and one of them can be seen from their worship practices. The Indonesian Ulema Council (MUI) as a religious authority has issued a fatwa that supports the government's program in preventing the transmission of COVID-19. However, polarization occurred among the people, giving rise to new social categories that tended to be opposed to pro-government people. The methodology used is a religious sociology approach. The conclusion of this analysis is that Muslims are polarized in accepting government policies, namely; 1) irrational-passive groups, those whose views are not based on scientific logic and do not provide solutions in preventing the COVID-19 pandemic, 2) active-hating groups but the arguments given tend to be irrational, 3) rational groups, but some are semi-rational and support government policies, 4) rational groups but shy in presenting their arguments, and 5) rational-active groups supporting government policies.


2017 ◽  
Vol 101 (5-6) ◽  
pp. 1066-1067 ◽  
Author(s):  
M. Norooz-Abadian ◽  
H. Sharifi
Keyword(s):  

1989 ◽  
Vol 33 (1) ◽  
pp. 103-131 ◽  
Author(s):  
Walter Feit ◽  
Gary M. Seitz
Keyword(s):  

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