Hostname: page-component-6bf8c574d5-qdpjg Total loading time: 0 Render date: 2025-02-27T01:01:39.907Z Has data issue: false hasContentIssue false
  • English
  • Français

ON LARGE ORBITS OF FINITE SOLVABLE GROUPS ON CHARACTERS

Part of: Representation theory of groups

Published online by Cambridge University Press:  07 February 2023

YONG YANG Open the ORCID record for YONG YANG [Opens in a new window]  and
JINBAO LI Open the ORCID record for JINBAO LI [Opens in a new window]
YONG YANG
Affiliation:
Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, Hubei 443002, PR China and Department of Mathematics, Texas State University, San Marcos, TX 78666, USA e-mail: yang@txstate.edu
JINBAO LI*
Affiliation:
Department of Mathematics, Suqian University, Jiangsu 223800, PR China
*
e-mail: leejinbao25@hotmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that if a solvable group A acts coprimely on a solvable group G, then A has a relatively ‘large’ orbit in its corresponding action on the set of ordinary complex irreducible characters of G. This improves an earlier result of Keller and Yang [‘Orbits of finite solvable groups on characters’, Israel J. Math. 199 (2014), 933–940].

Keywords

group actionirreducible charactersorbit structurelinear group

MSC classification

Primary: 20C20: Modular representations and characters
Secondary: 20C15: Ordinary representations and characters
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 108 , Issue 3 , December 2023 , pp. 438 - 442
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of 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.)

Footnotes

The project is partially supported by grants from the Simons Foundation (No. 499532, No. 918096) to the first author, Scientific Research Foundation for Advanced Talents of Suqian University (2022XRC069), the Science and Technology Research Program of Chongqing Municipal Education Commission (KJZD-K202001303) and the Natural Science Foundation of Chongqing, China (cstc2021jcyj-msxmX0511).

References

Keller, T. M. and Yang, Y., ‘Orbits of finite solvable groups on characters’, Israel J. Math. 199 (2014), 933–940.10.1007/s11856-013-0073-0CrossRefGoogle Scholar
Manz, O. and Wolf, T. R., Representations of Solvable Groups, London Mathematical Society Lecture Note Series, 185 (Cambridge University Press, Cambridge, 1993).10.1017/CBO9780511525971CrossRefGoogle Scholar
Moretó, A., ‘Large orbits of $p$ -groups on characters and applications to character degrees’, Israel J. Math. 146 (2005), 243–251.10.1007/BF02773535CrossRefGoogle Scholar
Qian, G. and Yang, Y., ‘Large orbit sizes in finite group actions’, J. Pure Appl. Algebra 225 (2021), Article no. 106458.10.1016/j.jpaa.2020.106458CrossRefGoogle Scholar
Yang, Y., ‘Orbits of the actions of finite solvable groups’, J. Algebra 321 (2009), 2012–2021.10.1016/j.jalgebra.2008.12.016CrossRefGoogle Scholar
Yang, Y., ‘On nilpotent group actions on the characters of solvable groups’, Algebr. Represent. Theory 23 (2020), 1–6.10.1007/s10468-018-9834-0CrossRefGoogle Scholar