دوره 17، شماره 1 - ( 1-1401 )
جلد 17 شماره 1 صفحات 151-145 |
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Moosavi S A. Groups whose Bipartite Divisor Graph for Character Degrees Has Five Vertices. IJMSI 2022; 17 (1) :145-151
URL: http://ijmsi.ir/article-1-1390-fa.html
URL: http://ijmsi.ir/article-1-1390-fa.html
Groups whose Bipartite Divisor Graph for Character Degrees Has Five Vertices. مجله علوم ریاضی و انفورماتیک. 1401; 17 (1) :145-151
چکیده:
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.
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