Concept

Baby monster group

Summary
In the area of modern algebra known as group theory, the baby monster group B (or, more simply, the baby monster) is a sporadic simple group of order :   241313567211131719233147 : = 4154781481226426191177580544000000 : = 4,154,781,481,226,426,191,177,580,544,000,000 : ≈ 4. B is one of the 26 sporadic groups and has the second highest order of these, with the highest order being that of the monster group. The double cover of the baby monster is the centralizer of an element of order 2 in the monster group. The outer automorphism group is trivial and the Schur multiplier has order 2. History The existence of this group was suggested by Bernd Fischer in unpublished work from the early 1970s during his investigation of {3,4}-transposition groups: groups generated by a class of transpositions such that the product of any two elements has order at most 4. He investigated its properties and computed its character table. The first construction of the baby monster
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