Some group theoretical mass formulae
Group Theory
2021-01-01 v2
Abstract
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 -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.
Cite
@article{arxiv.1509.03151,
title = {Some group theoretical mass formulae},
author = {Avinoam Mann},
journal= {arXiv preprint arXiv:1509.03151},
year = {2021}
}
Comments
There are some gaps in the proofs of Th.1 and Th.4, and the statement of these results need to be changed and correct proofs given