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RATIONAL NEARLY SIMPLE GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  21 September 2020

FARIDEH SHAFIEI Open the ORCID record for FARIDEH SHAFIEI [Opens in a new window] ,
MOHAMMAD REZA DARAFSHEH Open the ORCID record for MOHAMMAD REZA DARAFSHEH [Opens in a new window]  and
FARROKH SHIRJIAN Open the ORCID record for FARROKH SHIRJIAN [Opens in a new window]
FARIDEH SHAFIEI*
Affiliation:
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran School of Mathematics, Institute for Research in Fundamental Sciences (IPM), 19395-5746, Tehran, Iran
MOHAMMAD REZA DARAFSHEH*
Affiliation:
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
FARROKH SHIRJIAN*
Affiliation:
Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran
*
e-mail: [email protected]
e-mail: [email protected]
e-mail: [email protected]
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Abstract

A finite group whose irreducible complex characters are rational-valued is called a rational group. The aim of this paper is to determine the rational almost simple and rational quasi-simple groups.

Keywords

rational groupsalmost simple groupsquasi-simple groups

MSC classification

Primary: 20C15: Ordinary representations and characters
Secondary: 20D05: Finite simple groups and their classification
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 3 , June 2021 , pp. 475 - 485
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

The first-named author gladly acknowledges the financial support of the University of Tehran during the course of this work. The research of the first-named author was also in part supported by a grant from IPM (No. 99200027). The third-named author was in part supported by the Grant No. 98012009 from the Iranian National Science Foundation (INSF).

References

Bosma, W., Cannon, J. and Playoust, C., ‘The Magma algebra system I: The user language’, J. Symb. Comput. 24(3–4) (1997), 235–265.CrossRefGoogle Scholar
Bray, J. N., Holt, D. F. and Roney-Dougal, C. M., The Maximal Subgroups of the Low-Dimensional Finite Classical Groups, London Mathematical Society Lecture Note Series, 407 (Cambridge University Press, Cambridge, UK, 2013).CrossRefGoogle Scholar
Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., Atlas of Finite Groups. Maximal Subgroups and Ordinary Characters for Simple Groups, with Computational Assistance from J. G. Thackray (Oxford University Press, Eynsham, UK, 1985).Google Scholar
Darafsheh, M. R. and Sharifi, H., ‘Frobenius $\mathbb{Q}$ -groups’, Arch. Math. (Basel) 83(2) (2004), 102–105.CrossRefGoogle Scholar
Feit, W. and Seitz, G. M., ‘On finite rational groups and related topics’, Illinois J. Math. 33(1) (1989), 103–131.CrossRefGoogle Scholar
Grechkoseeva, M. A., ‘On orders of elements of finite almost simple groups with linear or unitary socle’, J. Group Theory 20(6) (2017), 1191–1222.CrossRefGoogle Scholar
Huppert, B., Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, 134 (Springer-Verlag, Berlin--New York, 1967).CrossRefGoogle Scholar
Malle, G. and Testerman, D., Linear Algebraic Groups and Finite Groups of Lie Type, Cambridge Studies in Advanced Mathematics, 133 (Cambridge University Press, Cambridge, UK, 2011).CrossRefGoogle Scholar
Martin Isaacs, I., Character Theory of Finite Group, Pure and Applied Mathematics , 69 (Academic Press [Harcourt Brace Jovanovich Publishers], New York--London, 1976).Google Scholar
Navarro, G., ‘The McKay conjecture and Galois automorphisms’, Ann. Math. (2) 160(3) (2004), 1129–1140.CrossRefGoogle Scholar
The GAP Group, Gap—Groups, Algorithms, and Programming—A System for Computational Discrete Algebra , Version 4.11.0 (2020). Available online at https://www.gap-system.org.Google Scholar
Wilson, R. A., The Finite Simple Groups, Graduate Texts in Mathematics, 251 (Springer, London, 2009).CrossRefGoogle Scholar