Questions tagged [monster]
Questions about the Monster group, the largest of the sporadic simple groups. This group acts as symmetries on a vertex operator algebra whose graded dimension is the elliptic $j$-function.
21 questions
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What is the 67-bit circuit representation of the monster group?
From wikipedia we know the smallest permutation representation of the monster group is a permutation group acting on
$$M = 2^4 · 3^7 · 5^3 · 7^4 · 11 · 13^2 · 29 · 41 · 59 · 71 \approx 10^{20} \ \text{...
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Why does the monster group exist?
Recently, I was watching an interview that John Conway did with Numberphile. By the end of the video, Brady Haran asked John:
If you were to come back a hundred years after your death, what problem ...
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On level-$12$ of the McKay-Thompson series of the Monster and the Domb numbers
(This continues from level 10.) Given some moonshine functions $j_{N}$. There are nice descending and consistent relations for levels $6m$ with $m= 2,3,5,$
$$j_{12A} = \left(\sqrt{j_{12H}} + \frac{\...
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On level $10$ of the McKay-Thompson series of the Monster
(For brevity, the level-6 functions have been migrated to another post.)
I. Level-10 functions
Given the Dedekind eta function $\eta(\tau)$. To recall, for level-6,
$$j_{6A} = \left(\sqrt{j_{6B}} + \...
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Is there an extension of Ogg's Moonshine results to surfaces of Genus 1
Per here the first hints of moonshine appeared around 1974 when Andrew Ogg noticed that quotienting the hyperbolic plane by normalizers of the Hecke Congruence subgroups $\Gamma_{0}(p)$ has genus zero ...
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Kissing the Monster, or $196{,}560$ vs. $196{,}883$
The $D = 24$ kissing number is $196{,}560$, and the dimension of the smallest non-trivial complex representation of the Monster group is $196{,}883$. These two numbers are nearly but not quite equal, ...
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Monster group as automorphism group of a distributive lattice
It is known that every finite group is the automorphism group of a finite distributive lattice.
Question: What is the minimal order of a distributive lattice $L$ such that the automorphism group of $...
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Is $J_1$ a subquotient of the monster group?
Edit: I was able to make a 3D diagram of the happy family if anyone is interested!
https://www.youtube.com/watch?v=_4IjnIcECoQ
I'm working on a twitter thread about the monster group, because I saw ...
user141903
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What is the geometric shape of the Monster sporadic group?
Conway made the comment that the Monster group represents the symmetries of a shape in 196,883 dimensions, something like a "star you hang on a Christmas tree."
My question is, What do we know (or ...
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Where can I find a table of the exponents of the sporadic groups?
Is there a table showing Sporadic Groups and their exponents, and, perhaps, other basic properties.
In particular, I'm interested in what the exponent of the Monster Group is. (Obviously the order is ...
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Why do these two Monster-related calculations yield $163$?
Fact 1: (1979, Conway and Norton)$^{1}$
"There are $194-22-9=\color{blue}{163\,}$ $\mathbb{Z}$-independent McKay-Thompson series for the Monster."
Note: There are 194 (linear) irreducible ...
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71, the Monster, and c = 24 CFTs
The largest prime in the order of the Monster group is $71$. This number $71$ shows up at various places:
The minimal faithful representation has dimension $196883 = 47\cdot 59\cdot 71$.
The Monster ...
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Monstrous Langlands-McKay or what is bijection between conjugacy classes and irreducible representation for sporadic simple groups?
Context: The number of conjugacy classes equals to the number of irreducuble representations (over C) for any finite group. Moreover for the symmetric group and some other groups there is "good ...
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The largest primes in the monster group construction
The last three prime numbers in the factorization of the order of the Fischer Griess friendly monster group are 47, 59, 71. (https://en.wikipedia.org/wiki/Monster_group)
On the other hand, the monster ...
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Sporadic and Exceptional
I have been reading this recent paper of J.McKay and YH. He (they've written a number of papers recently, including a fun and joking one on 42 which overflow commented on) called "Sporadic and ...
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