Book:John F. Humphreys/A Course in Group Theory

Subject Matter

 * Group Theory

Contents

 * Preface (Liverpool, January 1996)


 * 1 Definitions and examples


 * 2 Maps and relations on sets


 * 3 Elementary consequences of the definitions


 * 4 Subgroups


 * 5 Cosets and Lagrange's Theorem


 * 6 Error-correcting codes


 * 7 Normal subgroups and quotient groups


 * 8 The Homomorphism Theorem


 * 9 Permutations


 * 10 The Orbit-Stabiliser Theorem


 * 11 The Sylow Theorems


 * 12 Applications of Sylow theory


 * 13 Direct products


 * 14 The classification of finite abelian groups


 * 15 The Jordan–Hölder Theorem


 * 16 Composition factors and chief factors


 * 17 Soluble groups


 * 18 Examples of soluble groups


 * 19 Semidirect products and wreath products


 * 20 Extensions


 * 21 Central and cyclic extensions


 * 22 Groups with at most 31 elements


 * 23 The projective special linear groups


 * 24 The Mathieu groups


 * 25 The classification of finite simple groups
 * 25.1 The classical groups
 * 25.1.1 The projective special linear groups
 * 25.1.2 The unitary groups
 * 25.1.3 The symplectic groups
 * 25.1.4 The orthogonal groups
 * 25.2 Groups of Lie type
 * 25.3 The sporadic groups


 * A Prerequisites from number theory and linear algebra
 * A.1 Number theory
 * A.2 Linear algebra and determinants


 * B Groups of order < 32


 * C Solutions to exercises


 * Bibliography


 * Index

Syndrome is Zero iff Vector is Codeword
Chapter $6$: Error-correcting codes:

Product with Inverse on Homomorphic Image is Group Homomorphism
Chapter $8$: The Homomorphism Theorem:

Cycle Decomposition of Permutation in $S_9$
Chapter $9$: Permutations:

Normal Subgroup of Group of Order $24$
Chapter $12$: Applications of Sylow Theory:

Groups of Order $30$
Chapter $13$: Direct products:

Groups of Order $30$: $C_3 \times D_5$
Chapter $13$: Direct products: