The Monstrous Moonshine Picture
Abstract
We describe the finite subgraph $\mathfrak{M}$ of Conway's Big Picture required to describe all $171$ genus zero groups appearing in monstrous moonshine. We determine the local structure of $\mathfrak{M}$ and give a purely grouptheoretic description of this picture, based on powers of the conjugacy classes $24J$ and $8C$. We expect similar results to hold for umbral moonshine groups and give the details for the largest Mathieu group $M_{24}$.
 Publication:

arXiv eprints
 Pub Date:
 April 2018
 arXiv:
 arXiv:1804.04127
 Bibcode:
 2018arXiv180404127L
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Quantum Algebra;
 Mathematics  Rings and Algebras;
 Mathematics  Representation Theory