= Let G be a free abelian group with rank (G) {x1,...,n} be a basis for G and Y 1 aiji. Show that det (aij) X = n and H

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Let G Be A Free Abelian Group With Rank G X1 N Be A Basis For G And Y 1 Aiji Show That Det Aij X N And H 1 (209.96 KiB) Viewed 171 times

= Let G be a free abelian group with rank (G) {x1,...,n} be a basis for G and Y 1 aiji. Show that det (aij) X = n and H be a subgroup of G with rank(H) = n. Let {y₁,..., Yn} be a basis for H. Let [Id]} = (aij)n×n, is independent of the choices of X and Y. Deduce = n where yj = that |det(aij)| = [G : H].