Table of Contents
What is the monster in group theory?
The monster can be realized as a Galois group over the rational numbers, and as a Hurwitz group. The monster is unusual among simple groups in that there is no known easy way to represent its elements. This is not due so much to its size as to the absence of “small” representations.
How was the monster group found?
The first of the sporadic simple groups was discovered in the nineteenth century by French mathematician Émile Mathieu. It wasn’t until 1973 that two mathematicians—Bob Griess at the University of Michigan and Bernd Fischer at Universität Bielefeld—independently predicted the existence of the monster.
How many elements does the monster have?
It contains the following number of elements: 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 (more than the number of quarks in the Sun).
How many simple groups are there?
The following table is a complete list of the 18 families of finite simple groups and the 26 sporadic simple groups, along with their orders. Any non-simple members of each family are listed, as well as any members duplicated within a family or between families.
Is Za simple group?
Similarly, the additive group of the integers (Z, +) is not simple; the set of even integers is a non-trivial proper normal subgroup. One may use the same kind of reasoning for any abelian group, to deduce that the only simple abelian groups are the cyclic groups of prime order.
What number is the monster?
The least number of dimensions in which the Monster group can act non-trivially is 196,883. This number is 47.59. 71, the product of the three largest prime numbers dividing the size of the Monster, but its main point of interest is that by adding 1 we obtain 196,884.
What is strong against monster legends?
The Circle of Power All Elements are strong against an element and weak against an other, except Special, which is strong and weak to no other element. Example: Thunder is strong against Water, but weak against Earth. Fire is strong against Nature, but weak against Water, etc.
Are there infinite simple groups?
Classification. There is as yet no known classification for general (infinite) simple groups, and no such classification is expected.