Finally, the Monster group itself is considered to be in this generation.

The Monster group is the largest of these sporadic groups.

The order of the Monster group is divisible by p.

It centralizes an element of order 7 in the Monster group.

Cox joins your monsters group after finishing the game with Lady.

A Tarski monster group is periodic, but not locally finite.

This construction is much harder, but has the advantage of proving that the monster group acts naturally on it.

The Conway groups in turn are found in the Monster group.

The theory of modular forms shows how the E8 is connected to the Monster group.

J is the smallest of the 6 sporadic simple groups called the pariahs, because they are not found within the Monster group.

He constructed the monster group using the Griess algebra.

For example, the centralizer of an involution of type 2B in the monster group has structure 2.

He has a number of contacts and allies within Nightwatch, the monster groups, and other groups.

During battle other players' groups and other monster groups may join in to a maximum of three groups on each side.

"There's an analogous situation in the theory of finite groups-a monster group that contains many smaller ones as subgroups."

The third generation consists of subgroups which are closely related to the Monster group M:

In group theory, the Monster group (shortened to M or F) is important.

Ellis also introduced the concept of a multiverse to the series, drawing upon the mathematical concept known as the Monster group for inspiration.

(Interestingly, only the largest sporadic group, the monster group is big enough to incorporate the constraints for the Standard Model).

It is now known that lying behind monstrous moonshine is a certain conformal field theory having the Monster group as symmetries.

Of the 26 sporadic groups, 20 can be seen inside the Monster group as subgroups or quotients of subgroups (sections).

There is even a polynomial with integral coefficients whose Galois group is the Monster group.

This can be used to show that many finite simple groups, including the monster group, are Galois groups of extensions of the rationals.

The monster group is the largest of these sporadic groups and contains all but six of the other sporadic groups as subquotients.

In mathematical group theory, the term pariah was introduced by to refer to the six sporadic simple groups that are not subquotients of the monster group.