Groups whose character degree graph has diameter three
Abstract
Let \(G\) be a finite group, and let \((G)\) denote the prime graph built on the set of degrees of the irreducible complex characters of \(G\). It is well known that, whenever \((G)\) is connected, the diameter of \((G)\) is at most \(3\). In the present paper, we provide a description of the finite solvable groups for which the diameter of this graph attains the upper bound. This also enables us to confirm a couple of conjectures proposed by M.L. Lewis.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.