Finite Geometry Notes   | Home | Site Map | Author |

Noncontinuous Groups
by Steven H. Cullinane

A group of geometric transformations, all of which are continuous, may be called a discrete group or discontinuous group when the group is finite.

(Do web searches for "discrete group" and "discontinuous group" for finer shades of meaning.)

What, then, should a finite group of geometric transformations, some of which are discontinuous, be called?

The phrase "noncontinous group" seems apt.

Examples of noncontinuous groups:

Groups of discrete versions of chaotic maps (cf. Wikipedia articles).

The diamond theorem

Finite geometry of the square and cube

Pattern groups

Ivars Peterson on "Scrambled Grids" (Aug. 28, 2000)

The Mathieu group M24 acting on the Miracle Octad Generator of R. T. Curtis. This is on the cover of Griess's Twelve Sporadic Groups

Cover of Griess's 'Twelve Sporadic Groups'

Page created October 16, 2009