𝒫-characters and the structure of finite solvable groups

Jiakuan Lu 1 , Kaisun Wu 2 , and Wei Meng 3
  • 1 School of Mathematics and Statistics, Guangxi Normal University, 541006, Guangxi, Guilin, P. R. China
  • 2 School of Mathematics and Statistics, Guangxi Normal University, 541006, Guangxi, Guilin, P. R. China
  • 3 School of Mathematics and Computing Science, Guilin University of Electronic Technology, 541006, Guangxi, Guilin, P. R. China
Jiakuan Lu
  • Corresponding author
  • School of Mathematics and Statistics, Guangxi Normal University, Guilin, 541006, Guangxi, P. R. China
  • Email
  • Search for other articles:
  • degruyter.comGoogle Scholar
, Kaisun Wu and Wei Meng
  • School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, 541006, Guangxi, P. R. China
  • Email
  • Search for other articles:
  • degruyter.comGoogle Scholar

Abstract

Let 𝐺 be a finite group. An irreducible character of 𝐺 is called a 𝒫-character if it is an irreducible constituent of (1H)G for some maximal subgroup 𝐻 of 𝐺. In this paper, we obtain some conditions for a solvable group 𝐺 to be 𝑝-nilpotent or 𝑝-closed in terms of 𝒫-characters.

  • [1]

    X. Chen, Weak M p M_{p}-groups, Comm. Algebra 48 (2020), no. 8, 3594–3596.

    • Crossref
    • Export Citation
  • [2]

    N. Du and M. L. Lewis, Codegrees and nilpotence class of 𝑝-groups, J. Group Theory 19 (2016), no. 4, 561–567.

  • [3]

    S. M. Gagola, and M. L. Lewis, A character-theoretic condition characterizing nilpotent groups, Comm. Algebra 27 (1999), no. 3, 1053–1056.

    • Crossref
    • Export Citation
  • [4]

    I. M. Isaacs, Large orbits in actions of nilpotent groups, Proc. Amer. Math. Soc. 127 (1999), no. 1, 45–50.

    • Crossref
    • Export Citation
  • [5]

    I. M. Isaacs, Character Theory of Finite Groups, AMS Chelsea, Providence, 2006.

  • [6]

    I. M. Isaacs, Element orders and character codegrees, Arch. Math. (Basel) 97 (2011), no. 6, 499–501.

    • Crossref
    • Export Citation
  • [7]

    J. König, Solvability of generalized monomial groups, J. Group Theory 13 (2010), no. 2, 207–220.

  • [8]

    M. L. Lewis, Groups where all the irreducible characters are super-monomial, Proc. Amer. Math. Soc. 138 (2010), no. 1, 9–16.

    • Crossref
    • Export Citation
  • [9]

    L. Pang and J. Lu, Finite groups and degrees of irreducible monomial characters, J. Algebra Appl. 15 (2016), no. 4, Article ID 1650073.

  • [10]

    G. Qian, Y. Wang and H. Wei, Co-degrees of irreducible characters in finite groups, J. Algebra 312 (2007), no. 2, 946–955.

    • Crossref
    • Export Citation
  • [11]

    G. Qian and Y. Yang, Permutation characters in finite solvable groups, Comm. Algebra 46 (2018), no. 1, 167–175.

    • Crossref
    • Export Citation
  • [12]

    Y. Yang and G. Qian, The analog of Huppert’s conjecture on character codegrees, J. Algebra 478 (2017), 215–219.

    • Crossref
    • Export Citation
Purchase article
Get instant unlimited access to the article.
$42.00
Log in
Already have access? Please log in.


or
Log in with your institution

Journal + Issues

Search