What is Monster group?
{{Groups}} In [[math]], there are many subjects. One of these is [[group theory]]. In group theory, the '''Monster group''' (shortened to ''M'' or ''F''<sub>1</sub>) is important. It is also called the Fischer-Griess Monster, or the Friendly Giant. It is a [[group (mathematics)|group]] of a [[Finite set|finite]] number of elements, which is equal to: :&nbsp;&nbsp;&nbsp;808&thinsp;017&thinsp;424&thinsp;794&thinsp;512&thinsp;875&thinsp;886&thinsp;459&thinsp;904&thinsp;961&thinsp;710&thinsp;757&thinsp;005&thinsp;754&thinsp;368&thinsp;000&thinsp;000&thinsp;000 : = 2<sup>46</sup> · 3<sup>20</sup> · 5<sup>9</sup> · 7<sup>6</sup> · 11<sup>2</sup> · 13<sup>3</sup> · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71 : ≈ 8 · 10<sup>53</sup>. It is a ''[[simple group]]''. Simple groups are very important in group theory. They are not made out of other groups, and other groups are always made out of combinations of them. A [[normal subgroup]] is an important part of a group. Simple groups have no [[normal subgroup]]s except the unimportant [[identity element]], and themselves. The finite simple groups have been completely classified (the [[classification of finite simple groups]]). There are two kinds of [[finite simple groups]] in the [[list of finite simple groups]]. The first kind has 18 [[countably]] infinite families. The second kind has 26 [[sporadic groups]]. They are not as systematic. The Monster group is the largest of these sporadic groups. It contains all but six of the other sporadic groups inside of it. [[Robert Griess]] has called these six exceptions [[pariah group|pariahs]]. The rest make up the '''happy family'''. ==Other websites== * [http://mathworld.wolfram.com/MonsterGroup.html MathWorld: Monster Group] * [http://brauer.maths.qmul.ac.uk/Atlas/v3/spor/M/ Atlas of Finite Group Representations: Monster group] {{DEFAULTSORT:Monster Group}} [[Category:Group theory]]