GL(2,p) and GL(3,3) Acting on Points

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

The two-dimensional space contains nine points: (0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,1), and (2,2). The 48 invertible 2×2 matrices over form the general linear group known as . They act on by matrix multiplication modulo 3, permuting the nine points. More generally, is the set of invertible matrices over the field , where is prime With (0,0) shifted to the center, the matrix actions on the nine points make symmetrical patterns.

Contributed by: Ed Pegg Jr (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

detailSectionParagraph


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send