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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
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