Corpus ID: 119660158

The Monstrous Moonshine Picture

@article{Bruyn2018TheMM,
  title={The Monstrous Moonshine Picture},
  author={L. L. Bruyn},
  journal={arXiv: Group Theory},
  year={2018}
}
  • L. L. Bruyn
  • Published 2018
  • Mathematics
  • arXiv: Group Theory
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 group-theoretic 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 $M_{24}$. 
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