The group transfer theorem (Q1345857)

The group transfer theorem was formulated by Artin (1927) and Schreier (1926) as a reduction to the Principal Ideal Theorem in algebraic number theory. It states: if the commutator quotient group \(G/G'\) of a finitely generated metabelian group \(G\) is finite then the transfer map from \(G\) to \(G'\) is trivial. We give an elementary proof of this theorem whose main feature is an easy proposition on the determinant of a certain matrix over a finitely presented commutative ring.