Finite groups of 2 X 2 integer matrices

Date of Publication

2002

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Abstract/Summary

This thesis is based mainly on Sections 1 to 5 of the article "Finite Groups of 2 X 2 Integer Matrices" by George Mackiw which appeared in Mathematics Magazine, Volume 69 (1996). This study was motivated by a presentation intended to show that the dihedral group D6 of symmetries of the hexagon can be realized as a group of invertible 2 x 2 matrices with real number coefficients. It discusses some of the properties of the general linear group GL(2,Z0, the set of invertible 2 x 2 integer matrices whose inverses also have integer entries and some properties of the minimum polynomial of a matrix. The Hamilton-Cayley Theorem were used to prove some of these properties. The special linear group SL(2,Z) is the subgroup of all matrices in GL(2,Z) with determinant 1. In this thesis, the order of SL(2,Z) is computed and its elements are enumerated. The main result in this thesis states that a finite group G can be represented as a group of invertible 2 x 2 integer matrices if and only if G is isomorphic to the subgroup of D4 or D6.

Abstract Format

html

Language

English

Format

Print

Accession Number

TU11095

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

70 leaves

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