Some finite abelian group theory and some q-series identities

Abstract

For a fixed odd prime $\ell$, we present new families of identities defined on various subposets of the poset of isomorphism classes of finite abelian $\ell$-groups, generalizing identities of Hall and Cohen-Lenstra. We also present a $q$-series identity.

8 pages, simplified proof of Corollary 4.2, updated references

References in corpus (1)

• Random matrices, the Cohen-Lenstra heuristics, and roots of unity

Cited by in corpus (1)

• A weighted Möbius function