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FINITE SOLVABLE GROUPS WITH DISTINCT MONOMIAL CHARACTER DEGREES

Part of: Representation theory of groups

Published online by Cambridge University Press:  04 September 2019

GUOHUA QIAN  and
YONG YANG
GUOHUA QIAN*
Affiliation:
Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu215500, China email ghqian2000@163.com
YONG YANG*
Affiliation:
Department of Mathematics, Texas State University, San Marcos, TX78666, USA Key Laboratory of Group and Graph Theories and Applications, Chongqing University of Arts and Sciences, Chongqing402160, China email yang@txstate.edu
*
✉ email ghqian2000@163.com
✉ email yang@txstate.edu
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Abstract

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

Keywords

solvable groupsmonomial characterscharacter degrees

MSC classification

Primary: 20C15: Ordinary representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 108 , Issue 3 , June 2020 , pp. 387 - 401
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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Footnotes

†

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).

References

Berkovich, Y., ‘Finite solvable groups in which only two nonlinear irreducible characters have equal degrees’, J. Algebra 184 (1996), 584–603.Google Scholar
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), 955–959.Google Scholar
Berkovich, Y. and Kazarin, L., ‘Finite nonsolvable groups in which only two nonlinear irreducible characters have equal degrees’, J. Algebra 184 (1996), 538–560.Google Scholar
Chillag, D. and Herzog, M., ‘Finite groups with almost distinct character degrees’, J. Algebra 319 (2008), 716–729.Google Scholar
Djokovic, D. Z. and Malzan, J., ‘Imprimitive irreducible complex characters of the alternating group’, Canad. J. Math. 28(6) (1976), 1199–1204.Google Scholar
Dolfi, S., Navarro, G. and Tiep, P. H., ‘Finite groups whose same degree characters are Galois conjugate’, Israel J. Math. 198 (2013), 283–331.Google Scholar
Dolfi, S. and Yadav, M. K., ‘Finite groups whose nonlinear irreducible characters of the same degree are Galois conjugate’, J. Algebra 452 (2016), 1–16.Google Scholar
Huppert, B., Endliche Gruppen I (Springer, Berlin, 1967).Google Scholar
Isaacs, I. M., Character Theory of Finite Groups (Academic Press, New York, 1976).Google Scholar
Qian, G., Wang, Y. and Wei, H., ‘Finite solvable groups with at most two nonlinear irreducible characters of each degree’, J. Algebra 320 (2008), 3172–3186.Google Scholar
Seitz, G. M., ‘Finite groups having only one irreducible representation of degree greater than one’, Proc. Amer. Math. Soc. 19 (1968), 459–461.Google Scholar
Wu, Y. and Zhang, P., ‘Finite solvable groups whose character graphs are trees’, J. Algebra 308(2) (2007), 536–544.Google Scholar