Does someone know how to find the size of the factor group below?
For B an nXn nonsingular integer matrix, let M(B) be the integer linear combinations of the B-columns. Let M(I) be the n-dimensional integer vectors. Treat both as additive abelian groups.
It is known that the factor group M(I) / M(B) has size | det(B) |. Although I have an arithmetic proof that removes the matter from group theory, I want to stay in group theory (if possible). Any ideas or references? Thanks.