A brief journey through extensions of rational groups

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.

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Structure of solvable rational groups

Proceedings of the London Mathematical Society ◽

10.1112/s0024611504015035 ◽

2005 ◽

Vol 90 (02) ◽

pp. 439-471 ◽

Cited By ~ 1

Author(s):

Hegedus Pál

Keyword(s):

Rational Groups

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Non-Abelian composition factors of m-rational groups

Journal of Algebra ◽

10.1016/j.jalgebra.2017.05.015 ◽

2017 ◽

Vol 485 ◽

pp. 288-309 ◽

Cited By ~ 2

Author(s):

Stephen Trefethen

Keyword(s):

Composition Factors ◽

Rational Groups

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Polarization of the Muslim community towards government policies in overcoming the COVID-19 pandemic in Indonesia

Linguistics and Culture Review ◽

10.21744/lingcure.v5ns1.1449 ◽

2021 ◽

Vol 5 (S1) ◽

pp. 642-652

Author(s):

Ahmad Zain Sarnoto ◽

Lamya Hayatina

Keyword(s):

Government Policies ◽

Religious Authority ◽

Muslim Community ◽

Social Categories ◽

The People ◽

Worship Practices ◽

Rational Groups

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.

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