
the monster graph and McKay’s observation
While the verdict on a neolithic Scottish icosahedron is still open, let us recall Kostant’s grouptheoretic construction of the icosahedron from its rotationsymmetry group $A_5 $. The alternating group $A_5 $ has two conjugacy classes of order 5 elements, both consisting of exactly 12 elements. Fix one of these conjugacy classes, say $C $ and […]

the future of this blog (2)
is decided : I’ll keep maintaining this URL until newyear’s eve. At that time I’ll be blogging here for 5 years… The few encounters I’ve had with architects, taught me this basic lesson of life : the main function of several rooms in a house changes every 5 years (due to children and yourself getting…

what does the monster see?
The Monster is the largest of the 26 sporadic simple groups and has order 808 017 424 794 512 875 886 459 904 961 710 757 005 754 368 000 000 000 = 2^46 3^20 5^9 7^6 11^2 13^3 17 19 23 29 31 41 47 59 71. It is not so much the size…

Looking for F_un
There are only a handful of human activities where one goes to extraordinary lengths to keep a dream alive, in spite of overwhelming evidence : religion, theoretical physics, supporting the Belgian football team and … mathematics. In recent years several people spend a lot of energy looking for properties of an elusive object : the…

Farey symbols of sporadic groups
John Conway once wrote : There are almost as many different constructions of $M_{24} $ as there have been mathematicians interested in that most remarkable of all finite groups. In the inguanodon post Ive added yet another construction of the Mathieu groups $M_{12} $ and $M_{24} $ starting from (half of) the Farey sequences and…

Iguanodon series of simple groups
Bruce Westbury has a page on recent work on series of Lie groups including exceptional groups. Moreover, he did put his slides of a recent talk (probably at MPI) online. Probably, someone considered a similar problem for simple groups. Are there natural constructions leading to a series of finite simple groups including some sporadic groups…

The Mathieu groupoid (1)
Conway’s puzzle M(13) is a variation on the 15puzzle played with the 13 points in the projective plane $\mathbb{P}^2(\mathbb{F}_3) $. The desired position is given on the left where all the counters are placed at at the points having that label (the point corresponding to the hole in the drawing has label 0). A typical…

neverendingbooksgeometry (2)
Here pdffiles of older NeverEndingBooksposts on geometry. For more recent posts go here.

NeverEndingBooksgroups
Here a collection of pdffiles of NeverEndingBooksposts on groups, in reverse chronological order.