# 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 $SL(2,3)$.

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Capsule Course Topic(s):
Linear Algebra | Matrix Algebra
Linear Algebra | Matrix Invertibility