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.It is a simple group, meaning it ...

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.It is a simple group, meaning it does not have any proper non-trivial normal subgroups (that is, the only non-trivial normal subgroup 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.The monster group is one of two principal constituents in the Monstrous moonshine conjecture by Conway and Norton, which relates discrete and non-discrete mathematics and was finally proved by Richard Borcherds in 1992.

In this setting, the monster group is visible as the automorphism group of the monster module, a vertex operator algebra, an infinite dimensional algebra containing the Griess algebra, and acts on the monster Lie algebra, a generalized Kac–Moody algebra.

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