Subgroups of a finitely generated abelian group

Office_Shredder

Can you do the case where G is generated by one element?

Then the inductive step: If the result is true for when G is generated by up to n elements, suppose that G is generated by n+1 elements a₁,...,a_n+1. Let H be a subgroup of G. What can we say about H by examining G/<a_n+1>?

Office_Shredder Blog Entries: 1 Recognitions: Homework Help	Can you do the case where G is generated by one element? Then the inductive step: If the result is true for when G is generated by up to n elements, suppose that G is generated by n+1 elements a₁,...,a_n+1. Let H be a subgroup of G. What can we say about H by examining G/<a_n+1>?