Inducing characters of prime power degree (Q1591248)

The main result proved in this paper is the following Theorem A. Let \(G\) be a \(p\)-solvable finite group, where \(p\) is an odd prime number. Suppose \(\chi\in\text{Irr}(G)\) is a character of \(p\)-power degree less than or equal to \(p^p\). Then every primitive character inducing \(\chi\) has the same degree. This paper is to be recommended, just by its usage of several kinds of entities, like anisotropic modules, \(p\)-length theory, Brauer characters, and the like.