Square character degree graphs yield direct products

Abstract

If $G$ is a solvable group, we take $\Delta (G)$ to be the character degree graph for $G$ with primes as vertices. We prove that if $\Delta (G)$ is a square, then $G$ must be a direct product.

Cited by in corpus (4)

• Groups whose prime graphs have no triangles
• 4-Regular prime graphs of nonsolvable groups
• n-exact Character Graphs
• Bipartite divisor graph for the set of irreducible character degrees