Monster group

The Monster group is one of the 26 sporadic groups in group theory, a branch of mathematics. For the most with one of the two symbolic names and abbreviated group of monsters also the English names monster group, Fischer- Griess monster group or friendly giant group are often used. The unusual name of this group can be explained that it is the most powerful of all 26 sporadic groups by far.

Discovery history and characteristics

The sporadic groups are those finite simple groups that do not fit into one of the 18 families of finite simple groups. Of these there are 26 pieces, and the Monster group is under these by far the most powerful with a group of order

The order of the next largest sporadic group, the so-called Baby Monster group is about 4.1033.

The existence of the monster group was suggested in 1973 by Bernd Fischer and Robert L. Griess. 1982 succeeded in the construction of the Griess Monster group as automorphism group of a commutative, non-associative algebra on a 196 883 -dimensional space. 1979 formulated Simon Norton and John H. Conway, a number of assumptions about relationships between the Monster group and the j- function (" monstrous moonshine " ), for the proof of which English mathematician Richard E. Borcherds 1998, inter alia, the International Congress of Mathematicians in Berlin Fields Medal was awarded.

The divisor of the order of the Monster group are the powers of 15 supersingular primes ( sequence A002267 in OEIS ). The Monster group is a Galois group, ie it is the symmetry group of an algebraic equation and can be fully characterized by specifying this equation.