BabyMonsterGroupB

BabyMonsterGroupB[]

represents the sporadic simple baby monster group .

Details

Background & Context

  • BabyMonsterGroupB[] represents the baby monster group , which is a group of order TemplateBox[{2, 41}, Superscript].TemplateBox[{3, 13}, Superscript].TemplateBox[{5, 6}, Superscript].TemplateBox[{7, 2}, Superscript].11.13.17.18.32.31.47. It is one of the 26 sporadic simple groups of finite order.
  • The baby monster group is the second largest of the sporadic finite simple groups. It was introduced by Bernd Fischer in the early 1970s and explicitly constructed by Leon and Sims in the late 1970s. BabyMonsterGroupB was discovered while investigating so-called -transposition groups, i.e. groups generated by a class of transpositions such that the product of any two elements has order at most 4. has a double cover that is the centralizer of an element of order 2 in the monster group, a permutation representation on 13 571 955 000 symbols, and a faithful matrix representation of size 4370 over the field of two elements. Along with the other sporadic simple groups, the baby monster group played a foundational role in the monumental (and complete) classification of finite simple groups.
  • The usual group theoretic functions may be applied to BabyMonsterGroupB[], including GroupOrder, GroupGenerators, GroupElements and so on. However, while BabyMonsterGroupB[] is a permutation group, due its large order, an explicit permutation representation is impractical for direct implementation. As a result, a number of such group theoretic functions may return unevaluated when applied to it. A number of precomputed properties of the baby monster group are available via FiniteGroupData["BabyMonster","prop"].
  • BabyMonsterGroupB is related to a number of other symbols. BabyMonsterGroupB is one of the eight groups (along with FischerGroupFi22, FischerGroupFi23, FischerGroupFi24Prime, HeldGroupHe, HaradaNortonGroupHN, ThompsonGroupTh and MonsterGroupM) collectively referred to as the "third generation" of sporadic finite simple groups. It is also one of 20 so-called "happy" sporadic groups, which all appear as a subquotient of the monster group.

Examples

Basic Examples  (1)

Order of the baby monster group :

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See Also

PermutationGroup  MonsterGroupM

Tutorials

Introduced in 2010
(8.0)