TY - JOUR
T1 - Groups whose Bipartite Divisor Graph for Character Degrees Has Five Vertices
TT -
JF - IJMSI
JO - IJMSI
VL - 17
IS - 1
UR - http://ijmsi.ir/article-1-1390-en.html
Y1 - 2022
SP - 145
EP - 151
KW - Bipartite divisor graph
KW - Character degree
KW - Solvable group.
N2 - Let $G$ be a finite group and $cd^*(G)$ be the set of nonlinear irreducible character degrees of $G$. Suppose that $rho(G)$ denotes the set of primes dividing some element of $cd^*(G)$. The bipartite divisor graph for the set of character degrees which is denoted by $B(G)$, is a bipartite graph whose vertices are the disjoint union of $rho(G)$ and $cd^*(G)$, and a vertex $p in rho(G)$ is connected to a vertex $a in cd^*(G)$ if and only if $p|a$. In this paper, we investigate the structure of a group $G$ whose graph $B(G)$ has five vertices. Especially we show that all these groups are solvable.
M3 10.52547/ijmsi.17.1.145
ER -