TY - JOUR
ID - 21476
TI - On nonsolvable groups whose prime degree graphs have four vertices and one triangle
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Hafezieh, Roghayeh
AD - Department of Mathematics, Gebze Technical University, P.O.Box 41400, Gebze, Turkey
Y1 - 2018
PY - 2018
VL - 7
IS - 3
SP - 1
EP - 6
KW - prime degree graph
KW - irreducible character degree
KW - triangle
DO - 10.22108/ijgt.2017.21476
N2 - Let $G$ be a finite group. The prime degree graph of $G$, denoted by $Delta(G)$, is an undirected graph whose vertex set is $rho(G)$ and there is an edge between two distinct primes $p$ and $q$ if and only if $pq$ divides some irreducible character degree of $G$. In general, it seems that the prime graphs contain many edges and thus they should have many triangles, so one of the cases that would be interesting is to consider those finite groups whose prime degree graphs have a small number of triangles. In this paper we consider the case where for a nonsolvable group $G$, $Delta(G)$ is a connected graph which has only one triangle and four vertices.
UR - https://ijgt.ui.ac.ir/article_21476.html
L1 - https://ijgt.ui.ac.ir/article_21476_7aa9bd067cc2235a1faa46dd8f4728af.pdf
ER -