Monster group facts for kids

Group theory

Group theory Basic notions Subgroup Normal subgroup Quotient group Group homomorphism (semi-)direct product Discrete groups Classification of finite simple groups Cyclic group Zn Alternating group An Sporadic groups Mathieu group M11..12,M22..24 Conway group Co1..3 Janko group J1, 2, 3, 4 Fischer group F22..24 Baby Monster group B Monster group M Other finite groups Symmetric group, Sn Dihedral group, Dn Infinite groups The integers, Z Modular groups, PSL(2,Z) and SL(2,Z) Topological groups Lie group General linear group GL(n) Special linear group SL(n) Orthogonal group O(n) Special orthogonal group SO(n) Unitary group U(n) Special unitary group SU(n) Symplectic group Sp(n) G2 F4 E6 E7 E8 Lorentz group Poincaré group Infinite dimensional groups conformal group diffeomorphism group Loop group Quantum group O(∞) SU(∞) Sp(∞)

The Monster group is a very special and huge group in math. People also call it the Fischer-Griess Monster or the Friendly Giant. It's a type of group that has a specific, limited number of elements. This number is incredibly large!

The Monster group is one of the biggest and most complex objects in a part of math called group theory. It's so big that its "order" (the number of elements it has) is:

80,801,742,479,451,287,588,645,990,496,171,075,700,575,436,800,000,000

That's about 8 followed by 53 zeros!

This group is also known as a simple group. Simple groups are like the "building blocks" for all other groups. They are special because they only have two very basic parts inside them: the "identity element" (which is like the number zero in addition, or one in multiplication) and the group itself.

Understanding Finite Simple Groups

Mathematicians have worked hard to list and understand all the different types of finite simple groups. This big project is called the classification of finite simple groups. They found two main kinds of these groups.

Families of Simple Groups

The first kind of simple groups are organized into 18 large "families." Think of these families like different types of animals, where each family has many members that share similar features. These families have an endless number of groups within them.

Sporadic Groups

The second kind of simple groups are called sporadic groups. There are 26 of these. They are called "sporadic" because they don't fit neatly into the big families. They are unique and don't follow a simple pattern. The Monster group is the largest of all these sporadic groups.

The Happy Family and Pariahs

The Monster group is so big and important that it actually contains almost all the other sporadic groups inside it! Out of the 26 sporadic groups, the Monster group includes all but six of them. These six groups that are not part of the Monster group are sometimes called "pariahs." The rest of the sporadic groups, which are found inside the Monster, are playfully known as the happy family.

See also

A friendly robot, like the Friendly Giant!

• What is Group Theory?
• What is a Simple Group?
• In Spanish: Grupo monstruo para niños