2015/09/10 by Avinoam Mann, Mann, Avinoam
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.1509.03151
openalex publication_date 2015/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A 'mass formula' is a formula involving a sum of reciprocals of automorphism groups orders. We provide several such formulae, e.g. ones involving covering groups of finite groups. Others generalize a formula of P.Hall, repalcing the class of abelian p-groups by subclasses, or by isoclinism classes of non-abelian groups, also by replacing automorphism groups by holomorphs, etc. We also note relations with the Rogers-Ramanujan and related identities.