Monster Group

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
Basic notions Subgroup Normal subgroup Quotient group Group homomorphism (Semi-)direct product group homomorphisms kernel image direct sum wreath product simple finite infinite continuous multiplicative additive cyclic abelian dihedral nilpotent solvable List of group theory topics Glossary of group theory
Finite groups Classification of finite simple groups Cyclic group Z_n Symmetric group S_n Dihedral group D_n Alternating group A_n Mathieu groups M₁₁ M₁₂ M₂₂ M₂₃ M₂₄ Conway groups Co₁ Co₂ Co₃ Janko groups J₁ J₂ J₃ J₄ Fischer groups F₂₂ F₂₃ F₂₄ Baby Monster group B Monster group M
Discrete groups and lattices Integers Z Lattice Modular groups PSL(2,Z) SL(2,Z)
Topological and Lie groups Solenoid Circle General linear GL(n) Special linear SL(n) Orthogonal O(n) Special orthogonal SO(n) Unitary U(n) Special unitary SU(n) Symplectic Sp(n) G₂ F₄ E₆ E₇ E₈ Lorentz Poincaré Conformal Diffeomorphism Loop Infinite dimensional Lie group O(∞) SU(∞) Sp(∞)
Algebraic groups Elliptic curve Linear algebraic group Abelian variety

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

Famous quotes containing the words monster and/or group:

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—Gilbert Keith Chesterton (1874–1936)

“Stripped of ethical rationalizations and philosophical pretensions, a crime is anything that a group in power chooses to prohibit.”
—Freda Adler (b. 1934)

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Finite Simple Groups

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