Coxeter Groups
There are a number of analogous results between algebraic groups and Coxeter groups – for instance, the number of elements of the symmetric group is, and the number of elements of the general linear group over a finite field is the q-factorial ; thus the symmetric group behaves as though it were a linear group over "the field with one element". This is formalized by the field with one element, which considers Coxeter groups to be simple algebraic groups over the field with one element.
Read more about this topic: Algebraic Group
Famous quotes containing the word groups:
“In America every woman has her set of girl-friends; some are cousins, the rest are gained at school. These form a permanent committee who sit on each other’s affairs, who “come out” together, marry and divorce together, and who end as those groups of bustling, heartless well-informed club-women who govern society. Against them the Couple of Ehepaar is helpless and Man in their eyes but a biological interlude.”
—Cyril Connolly (1903–1974)