Real characters and degrees

Israel Journal of Mathematics

Volumn 171, Issue 1, 2009, Pages 157-173

  Navarro, Gabriel ^a   Sanus, Lucia ^a   Tiep, Pham Huu ^b,c  

^a UNIVERSITY OF VALENCIA   (Spain)

^b UNIVERSITY OF FLORIDA   (United States)

^c The University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77749320905     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/s11856-009-0045-6     Document Type: Article

References (21)

1. R. Carter, Finite Groups of Lie type: Conjugacy Classes and Complex Characters, Wiley, Chichester, 1985.
2. D. Chillag and A. Mann, Nearly odd-order and nearly real finite groups, Communications in Algebra 26 (1998), 2041-2064.
3. J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, An ATLAS of Finite Groups, Clarendon Press, Oxford, 1985.
4. R. Dipper and J. Du, Harish-Chandra vertices, Journal für die Reine und Angewandte Mathematik 437 (1993), 101-130.
5. S. Dolfi, G. Navarro and Pham Huu Tiep, Primes dividing the degrees of the real characters of finite groups, Mathematishce Zeitschrift 259 (2008), 755-774.
6. W. Feit, Extending Steinberg characters, in Linear Algebraic Groups and their Representations, Los Angeles, CA, 1992, Contemporary Mathematics, 153, 1993), pp. 1-9.
7. The GAP group, GAP-groups, algorithms, and programming, Version 4. 4, 2004, http://www. gap-system. org.
8. D. Gorenstein, R. Lyons and R. Solomon, The Classification of the Finite Simple Groups, Number 3, Mathematical Surveys and Monographs, American Mathematial Society, Providence, 1994.
9. B. Huppert, Character Theory of Finite Groups, de Gruyter Expositions in Mathematics, 25, Walter de Gruyter & Co., Berlin, 1998.
10. I. M. Isaacs, Character Theory of Finite Groups, Dover, New York, 1994.
11. S. Iwasaki, On finite groups with exactly two real conjugate classes, Archiv der Mathematik (Basel) 33 (1979/80), 512-517.
12. P. B. Kleidman and M. W. Liebeck, The Subgroup Structure of the Finite Classical Groups, London Mathematical Society Lecture Note Series no. 129, Cambridge University Press, Cambridge, 1990.
13. F. Lübeck, Smallest degrees of representations of exceptional groups of Lie type, Communications in Algebra 29 (2001), 2147-2169.
14. A. Moretó and Pham Huu Tiep, Prime divisors of character degrees, Journal of Group Theory 11 (2008), 341-356.
15. A. Moretó and G. Navarro, Groups with three real valued irreducible characters, Israel Journal of Mathematics 163 (2008), 85-92.
16. G. Navarro and Pham Huu Tiep, Rational irreducible characters and rational conjugacy classes in finite groups, Transactions of the American Mathematical Society 360 (2008), 2443-2465.
17. G. Navarro and Pham Huu Tiep, Rational characters and degrees, submitted.
18. G. Navarro, L. Sanus, and Pham Huu Tiep, Groups with two real Brauer characters, Journal of Algebra 307 (2007), 891-898.
19. Pham Huu Tiep and A. E. Zalesskii, Minimal characters of the finite classical groups, Communications in Algebra 24 (1996), 2093-2167.
20. Pham Huu Tiep and A. E. Zalesskii, Real conjugacy classes in algebraic groups and finite groups of Lie type, Journal of Group Theory 8 (2005), 291-315.
21. K. Zsigmondy, Zur Theorie der Potenzreste, Monath. Math. Phys. 3 (1892), 265-284.