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Size of a Factor Group

Posted 9 years ago

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.

POSTED BY: Bruce Colletti

Look up the Smith normal form. That provides a link between the matrix algebra and the abelian group form.

POSTED BY: Daniel Lichtblau
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