Corollary 1

Tag 0748, permanent. Cite it as [Bourbaki, Tag 0748].

Algebra, chapter VII, § 4. Finitely generated modules over a principal ideal domain

— In a finite abelian group G, there exists an element whose order is the lcm of all the orders of elements of G; this order n is the first invariant factor of G.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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Corollary 3, § 4

Cites

Nothing.