maths document

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Group theory for Maths, Physics and ChemistrystudentsArjeh CohenRosane UshirobiraJan DraismaOctober 18, 20072Contents1 Introduction1.1 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2 Basic notions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55122 Permutation Groups2.1 Cosets and Lagrange . .2.2 Quotient groups and the2.3 Loyds puzzle . . . . . .2.4 Action of groups on sets. . . . . . . . .homomorphism. . . . . . . . .. . . . . . . . .3 Symmetry Groups in Euclidean Space3.1 Motivation . . . . . . . . . . . . . . .3.2 Isometries of n-space . . . . . . . . . .3.3 The Finite Subgroups of O(2, R) . . .3.4 The Finite Subgroups of O(3, R) . . ...... . . . .theorem. . . . .. . . . .....................................1717182228........................................3333354042................4 Representation Theory514.1 Linear representations of groups . . . . . . . . . . . . . . . . . . 514.2 Decomposing Displacements . . . . . . . . . . . . . . . . . . . . . 595 Character Tables5.1 Characters . . . . . . . . . . . . . . . .5.2 Orthogonality of irreducible characters5.3 Character tables . . . . . . . . . . . .5.4 Application: symmetry of vibrations .5.5 Notes . . . . . . . . . . . . . . . . . ................................

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