Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-22T17:38:44.789Z Has data issue: false hasContentIssue false
  • English
  • Français

$p$-DIVISIBILITY OF CO-DEGREES OF IRREDUCIBLE CHARACTERS

Part of: Representation theory of groups

Published online by Cambridge University Press:  07 April 2020

ROYA BAHRAMIAN Open the ORCID record for ROYA BAHRAMIAN [Opens in a new window]  and
NEDA AHANJIDEH Open the ORCID record for NEDA AHANJIDEH [Opens in a new window]
ROYA BAHRAMIAN
Affiliation:
Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran email [email protected]
NEDA AHANJIDEH*
Affiliation:
Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran email [email protected]
*
✉[email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

For a character $\unicode[STIX]{x1D712}$ of a finite group $G$, the co-degree of $\unicode[STIX]{x1D712}$ is $\unicode[STIX]{x1D712}^{c}(1)=[G:\text{ker}\unicode[STIX]{x1D712}]/\unicode[STIX]{x1D712}(1)$. We study finite groups whose co-degrees of nonprincipal (complex) irreducible characters are divisible by a given prime $p$.

Keywords

co-degree of a characterco-prime actionp-solvable groups

MSC classification

Primary: 20C15: Ordinary representations and characters
Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 1 , February 2021 , pp. 78 - 82
Check for updates
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alizadeh, F., Behravesh, H., Gaffarzadeh, M., Ghasemi, M. and Hekmatara, S., ‘Groups with few co-degrees of irreducible characters’, Comm. Algebra 47 (2019), 1147–1152.CrossRefGoogle Scholar
Bianchi, M., Chillag, D., Lewis, M. L. and Pacifici, E., ‘Character degree graphs that are complete graphs’, Proc. Amer. Math. Soc. 135(3) (2007), 671–676.CrossRefGoogle Scholar
Dolfi, S., ‘Orbits of permutation groups on the power set’, Arch. Math. 75 (2000), 321–327.CrossRefGoogle Scholar
Du, N. and Lewis, M. L., ‘Codegrees and nilpotence class of p-groups’, J. Group Theory 19(4) (2016), 561–568.CrossRefGoogle Scholar
Granville, A. and Ono, K., ‘Defect zero p-blocks for finite simple groups’, Trans. Amer. Math. Soc. 348 (1996), 331–347.CrossRefGoogle Scholar
Isaacs, I. M., Character Theory of Finite Groups (Dover, New York, 1994).Google Scholar
Lewis, M. L., Navarro, G., Tiep, P. H. and Tong-Viet, H. P., ‘p-Parts of character degrees’, J. Lond. Math. Soc. (2) 92(2) (2015), 483–497.CrossRefGoogle Scholar
Malle, G. and Zalesski, A., ‘Prime power degree representations of quasi-simple groups’, Arch. Math. 77(6) (2001), 461–468.CrossRefGoogle Scholar
Passman, D. S., ‘Groups with normal solvable Hall p ′-subgroups’, Trans. Amer. Math. Soc. 123 (1966), 99–111.Google Scholar
Qian, G., ‘A note on p-parts of character degrees’, Bull. Lond. Math. Soc. 50(4) (2018), 663–666.CrossRefGoogle Scholar
Qian, G., Wang, Y. and Wei, H., ‘Co-degrees of irreducible characters in finite groups’, J. Algebra 312 (2007), 946–955.CrossRefGoogle Scholar
Schmid, P., ‘Rational matrix groups of a special type’, Linear Algebra Appl. 71 (1985), 289–293.CrossRefGoogle Scholar
Schmid, P., ‘Extending the Steinberg representation’, J. Algebra Appl. 150 (1992), 254–256.CrossRefGoogle Scholar
Thompson, J., ‘Normal p-complements and irreducible characters’, J. Algebra 14 (1970), 129–134.CrossRefGoogle Scholar