by Steven H. Cullinane
A group of geometric transformations, all of which are continuous, may
be called a discrete group or discontinuous
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
The diamond theorem
the square and cube
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
Page created October 16,