You are here

Finite Groups of 2 x 2 Integer Matrices

by George Mackiw (Loyola College in Maryland)

This article originally appeared in:
Mathematics Magazine
December, 1996

Subject classification(s): Algebra and Number Theory | Linear Algebra
Applicable Course(s): 4.2 Mod Algebra I & II

The author shows that a finite group \(G\) can be represented as a group of invertible \( 2 \times 2\) integer matrices if and only if \(G\) is isomorphic to a subgroup of the dihedral groups \(D_4\) or \(D_6\).  Results are obtained by studying the relation between \(GL(2,\mathbf{Z})\) and \(SL(2,3)\).


A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.

To open this file please click here.

These pdf files are furnished by JSTOR.

Classroom Capsules would not be possible without the contribution of JSTOR.

JSTOR provides online access to pdf copies of 512 journals, including all three print journals of the Mathematical Association of America: The American Mathematical Monthly, College Mathematics Journal, and Mathematics Magazine. We are grateful for JSTOR's cooperation in providing the pdf pages that we are using for Classroom Capsules.

Capsule Course Topic(s):
Linear Algebra | Matrix Algebra
Linear Algebra | Matrix Invertibility
Average: 3 (132 votes)