Given a finite abelian $p$-group and its factorization into groups of the form $\mathbb{Z}/p^k\mathbb{Z}$, does anyone know of a formula that gives the number of subgroups of a certain index/order? As I'm sure such a formula would contain some nasty product or sum, is there a computer algebra system out there that knows how to compute this?
2026-03-28 19:30:49.1774726249
Formula or code to compute number of subgroups of a certain order of an abelian $p$-group
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