In a proof that I am reading the author wants to determine the order of the abelianized group $G / [G,G] $ of a group $G$ with a presentation with $n$ generators and $n$ relations.
The author states that this order is the absolute value of the determinant of the $n\times n$ relation matrix.
Can anyone give me a reference for such a theorem?
I'm not sure of the page number but you'll find it in D. L. Johnson's, "Presentation$\color{red}{s}$ of Groups" with ISBN 0 521 20829 7.