Characterizable and V-characterizable groups

Authors

  • Jinshan Zhang School of Science, Sichuan University of Science and Engineering, China
  • Xiu Liu School of Mathematics and Statistics, Zhaotong University, China
  • Dandan Liu School of Science, Sichuan University of Science and Engineering, China
  • Yanhua Huang School of Science, Sichuan University of Science and Engineering, China

DOI:

https://doi.org/10.7546/CRABS.2022.11.01

Keywords:

finite groups, characters, vanishing elements

Abstract

Let G be a finite group. The spectrum πe(G) is the set of all element orders of G. A vanishing element of G is an element g∈G such that χ(g)= 0 for some irreducible complex character χ of G. Denote by Vo(G) the set of the orders of vanishing elements of G. For a set Ω of positive integers, let h(Ω) (v(Ω)) be the number of isomorphism classes of finite group G such that πe(G)= Ω Vo(G)= Ω, respectively). A group G is called characterizable  (V-characterizable) if h(πe(G))= 1 (v(Vo(G))= 1, respectively). In this note, we discuss the relation between characterizable and  V-recognizable. Moreover, by an application of the the relation, we prove that the group M22 is V-characterizable.

 

Author Biographies

Jinshan Zhang, School of Science, Sichuan University of Science and Engineering, China

Mailing Address:
School of Science,
Sichuan University of Science
and Engineering
Zigong 643000, P. R. China

E-mail: zjscdut@163.com

Xiu Liu, School of Mathematics and Statistics, Zhaotong University, China

Mailing Address:
School of Mathematics and Statistics,
Zhaotong University
Zhaotong 657000, P. R. China

E-mail: 1105510794@qq.com

Dandan Liu, School of Science, Sichuan University of Science and Engineering, China

Mailing Address:
School of Science,
Sichuan University of Science
and Engineering
Zigong 643000, P. R. China

E-mail: 190085710@qq.com

Yanhua Huang, School of Science, Sichuan University of Science and Engineering, China

Mailing Address:
School of Science,
Sichuan University of Science
and Engineering
Zigong 643000, P. R. China

E-mail: maggie434100@163.com

Downloads

Published

30-11-2022

How to Cite

[1]
J. . Zhang, X. Liu, D. . Liu, and Y. . Huang, “Characterizable and V-characterizable groups”, C. R. Acad. Bulg. Sci. , vol. 75, no. 11, pp. 1551–1558, Nov. 2022.

Issue

Section

Mathematics