Finite Groups Whose Co-prime Order Graphs Have Positive Genus

Authors

  • Huani Li School of Sciences, Xi’an Technological University, China
  • Guo Zhong School of Information Science and Technology and Guangzhou Key Laboratory of Multilingual Intelligent Processing - Guangdong University of Foreign Studies, China
  • Xuanlong Ma School of Science, Xi’an Shiyou University, China

DOI:

https://doi.org/10.7546/CRABS.2022.09.03

Keywords:

co-prime order graph, genus, finite group

Abstract

Given a finite group G, the co-prime order graph of G is the simple undirected graph whose vertex set is G, and two distinct vertices x; y are adjacent if gcd(o(x); o(y)) = 1 or p, where p is a prime, and o(x) and o(y) are the orders of x and y, respectively. In this paper, we prove that, for a fixed positive integer k, there are finitely many finite groups whose co-prime order graphs have (non)orientable genus k. As applications, we classify all finite groups whose co-prime order graphs have (non)orientable genus one and two. 

Author Biographies

Huani Li, School of Sciences, Xi’an Technological University, China

Mailing Address:
School of Sciences,
Xi’an Technological University
710021 Xi’an, P. R. China

E-mail: lihuanilp@163.com

Guo Zhong, School of Information Science and Technology and Guangzhou Key Laboratory of Multilingual Intelligent Processing - Guangdong University of Foreign Studies, China

Mailing Address:
School of Information Science and Technology,
Guangdong University of Foreign Studies
510000 Guangzhou, P. R. China

and

Guangzhou Key Laboratory of
Multilingual Intelligent Processing,
Guangdong University of Foreign Studies
510000 Guangzhou, P. R. China

E-mail: zhong_guom@126.com

 

Xuanlong Ma, School of Science, Xi’an Shiyou University, China

Mailing Address:
School of Science,
Xi’an Shiyou University
710065 Xi’an, P. R. China

E-mail: xuanlma@mail.bnu.edu.cn

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Published

30-09-2022

How to Cite

[1]
H. Li, G. Zhong, and X. Ma, “Finite Groups Whose Co-prime Order Graphs Have Positive Genus”, C. R. Acad. Bulg. Sci., vol. 75, no. 9, pp. 1270–1278, Sep. 2022.

Issue

Section

Mathematics