On the average character degree of finite groups
Abstract
We prove that if the average of the degrees of the irreducible characters of a finite group G is less than 16/5, then G is solvable. This solves a conjecture of I.M. Isaacs, M. Loukaki, and the first author. We discuss related questions.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.