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FINITE SOLVABLE GROUPS WITH DISTINCT MONOMIAL CHARACTER DEGREES

  • GUOHUA QIAN (a1) and YONG YANG (a2) (a3)

Abstract

In this paper we classify the finite solvable groups in which distinct nonlinear monomial characters have distinct degrees.

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Copyright

Corresponding author

Footnotes

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Email addresses for correspondence: email ghqian2000@163.com, yang@txstate.edu.

Project supported by NSF of China (nos 11471054, 11671063, and 11871011), NSF of Jiangsu Province (no. BK20161265), Natural Science Foundation of Chongqing (cstc2016jcyjA0065, cstc2018jcyjAX0060), and a grant from the Simons Foundation (no. 499532).

Footnotes

References

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[1]Berkovich, Y., ‘Finite solvable groups in which only two nonlinear irreducible characters have equal degrees’, J. Algebra 184 (1996), 584603.
[2]Berkovich, Y., Chillag, D. and Herzog, M., ‘Finite groups in which the degrees of nonlinear irreducible characters are distinct’, Proc. Amer. Math. Soc. 115(4) (1992), 955959.
[3]Berkovich, Y. and Kazarin, L., ‘Finite nonsolvable groups in which only two nonlinear irreducible characters have equal degrees’, J. Algebra 184 (1996), 538560.
[4]Chillag, D. and Herzog, M., ‘Finite groups with almost distinct character degrees’, J. Algebra 319 (2008), 716729.
[5]Djokovic, D. Z. and Malzan, J., ‘Imprimitive irreducible complex characters of the alternating group’, Canad. J. Math. 28(6) (1976), 11991204.
[6]Dolfi, S., Navarro, G. and Tiep, P. H., ‘Finite groups whose same degree characters are Galois conjugate’, Israel J. Math. 198 (2013), 283331.
[7]Dolfi, S. and Yadav, M. K., ‘Finite groups whose nonlinear irreducible characters of the same degree are Galois conjugate’, J. Algebra 452 (2016), 116.
[8]Huppert, B., Endliche Gruppen I (Springer, Berlin, 1967).
[9]Isaacs, I. M., Character Theory of Finite Groups (Academic Press, New York, 1976).
[10]Qian, G., Wang, Y. and Wei, H., ‘Finite solvable groups with at most two nonlinear irreducible characters of each degree’, J. Algebra 320 (2008), 31723186.
[11]Seitz, G. M., ‘Finite groups having only one irreducible representation of degree greater than one’, Proc. Amer. Math. Soc. 19 (1968), 459461.
[12]Wu, Y. and Zhang, P., ‘Finite solvable groups whose character graphs are trees’, J. Algebra 308(2) (2007), 536544.
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Keywords

MSC classification

FINITE SOLVABLE GROUPS WITH DISTINCT MONOMIAL CHARACTER DEGREES

  • GUOHUA QIAN (a1) and YONG YANG (a2) (a3)

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