A note on transfer in finite group theory

Abstract

Finite groups are ubiquitous in mathematics and often arise as symmetry groups of objects. Consequently, finite group structure is of great interest. The transfer is a classical homomorphism of any finite group G into certain commutative sections of G. It has several basic applications in and has inspired new developments in finite group structure. In this article, we present a new characterization of the image of the transfer. Then we obtain new consequences and immediate proofs of old transfer consequences in finite group structure.