Abstract:
Finite simple groups occur naturally in certain infinite families, there are however 26 finite simple groups which are not members of any of them. These groups are therefore termed sporadic. The largest of these is the Monster, the simple group of Fischer and Griess.
The only construction that we know is as an automorphism group of a 196,883 dimensional algebra (Griess algebra).
Axial algebras generalise the Griess algebra and were introduced by Hall, Rehren and Shpectorov as a new algebraic object in order to find an easier way to study the Monster and, in general, finite simple groups.