Monster Groups and Other Sporadic Groups
Jill Horsfield (jbhorse@purdue.edu) Colin Mills (cwmills@purdue.edu) Andy Nelson (nelson70@purdue.edu)
1. What is a monster group?
-Definition: A monster group is a simple, sporadic group of finite order and contains all but 6 of the other sporadic groups
as subgroups. Its order is: 2^46 · 3^20 · 5^9 · 7^6 · 11^2 · 13^3 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71
=808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000
≈8 · 10^53
-Background: How did monster groups come about? When, who, and how did they reach this discovery?
In 1973, Bernd Fischer and Robert Griess predicted that monster group was a simple group containing baby monster groups.
Robert Griess discovered the order of this monster group only a couple months after the original discovery.
-What makes monster groups sporadic groups?
Sporadic groups are the finite simple groups (26) that don't fit into infinite families.
The largest sporadic group is the monster group.
2. Are there subgroups?
-What is the subgroup structure? -What are its primes and supersingular primes? -What is a baby monster group? -How does existence and uniqueness relate?
3. How does the Moonshine Theory relate to Monster Groups?
