Another Proof of a Theorem of J. A. Green

J. A. Green proved a theorem which is the converse of a theorem of R. Brauer (1955, Proc. Camb. Philos. Soc.51, 237–239). The present author gave another proof of the theorem by making an application of the characteristic class functions of a finite group. In this article we give another proof of the theorem which is easier than the two previous proofs of the theorem, by using the Mackey decomposition theorem.