In the mathematical field of group theory, the Monster group M or F1 (also known as the Fischer-Griess Monster, or the Friendly Giant) is a group of finite order:
| 246 · 320 · 59 · 76 · 112 · 133 · 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 · 1053. |
| Group theory |
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Basic notions
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Finite groups
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Discrete groups and lattices
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Topological and Lie groups
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Algebraic groups
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It is a simple group, meaning it does not have any non-trivial normal subgroups (that is, the only non-trivial normal subgroups is M itself).
The finite simple groups have been completely classified (see the Classification of finite simple groups). The list of finite simple groups consists of 18 countably infinite families, plus 26 sporadic groups that do not follow such a systematic pattern. The Monster group is the largest of these sporadic groups and contains all but six of the other sporadic groups as subquotients. Robert Griess has called these six exceptions pariahs, and refers to the others as the happy family.
Read more about Monster Group: Existence and Uniqueness, Representations, Moonshine, McKay's E8 Observation, Subgroup Structure
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