Corollary 2

Tag 0749, permanent. Cite it as [Bourbaki, Tag 0749].

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

— Any finite abelian group G whose order is not divisible by the square of any integer $> 1$ is cyclic. Let us keep to the notation of Th. 3. Then $p = 0$ since G is finite, and $q \leq 1$ , for otherwise the order of G would be divisible by $n_q^2$ . Hence G is cyclic.

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

Cited by

Nothing.

Cites

Th. 3