TY - JOUR
AU - Li, Huani
AU - Zhong, Guo
AU - Ma, Xuanlong
PY - 2022/09/30
Y2 - 2024/07/25
TI - Finite Groups Whose Co-prime Order Graphs Have Positive Genus
JF - Proceedings of the Bulgarian Academy of Sciences
JA - C. R. Acad. Bulg. Sci.
VL - 75
IS - 9
SE - Mathematics
DO - 10.7546/CRABS.2022.09.03
UR - https://proceedings.bas.bg/index.php/cr/article/view/151
SP - 1270-1278
AB - <p>Given a finite group G, the co-prime order graph of <em>G</em> is the simple undirected graph whose vertex set is <em>G</em>, and two distinct vertices <em>x; y</em> are adjacent if gcd<em>(o(x); o(y))</em> = 1 or <em>p,</em> where p is a prime, and <em>o(x)</em> and <em>o(y)</em> are the orders of <em>x</em> and<em> y</em>, respectively. In this paper, we prove that, for a fixed positive integer <em>k</em>, there are finitely many finite groups whose co-prime order graphs have (non)orientable genus <em>k</em>. As applications, we classify all finite groups whose co-prime order graphs have (non)orientable genus one and two. </p>
ER -