Induction theorems for finite groups including a common generalization of two classical theorems

摘要

Roquette proved results involving induction about rings related to the character rings of finite groups and consisting of functions that vanish outside a plus'-section; Kletzing did something similar for Q-characters. This paper gives new generalizations of these results involving K-characters for any field K of characteristic 0 as well as corresponding theorems for a set of primes. That these facts are useful is illustrated by showing that they imply a common generalization of the Witt-Berman and Artin induction theorems as well as results of Chen, Fan, Hu, Robinson, and Sin. (C) 2019 Elsevier Inc. All rights reserved.