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· 제목 : Topics in Finite Groups (Hardcover)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 일반
· ISBN : 9781792480003
· 쪽수 : 277쪽
· 출판일 : 2021-08-18
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 일반
· ISBN : 9781792480003
· 쪽수 : 277쪽
· 출판일 : 2021-08-18
목차
- 1 Introduction
- 1.1 Preliminary Definitions
- 1.2 Examples of Groups
- 1.3 Some Basic Group Concepts and Terminology
- 1.4 Cyclic Groups
- 1.5 Direct and Semidirect Product of Groups
- 1.5.1 Direct Product
- 1.5.2 Examples of Direct Product
- 1.5.3 Semidirect Product
- 1.5.4 Examples of Semidirect Product
- 1.6 Isomorphism, Homomorphism, and Automorphism
- 1.6.1 Isomorphism and Homomorphism
- 1.6.2 Examples of Isomorphic Groups
- 1.6.3 Homomorphism and Kernel of Homomorphism
- 1.6.4 Examples of Quotient Groups
- 1.6.5 Homomorphism/Isomorphism Theorems
- 1.6.6 Abelian p-groups
- 1.6.7 Composition Series of Finite Groups
- 1.6.8 Jordan–Hölder Theorem
- 1.6.9 Automorphism group of a group
- 1.6.10 The Group Z?n
- 2 Permutation Groups and Sylow Theorems
- 2.1 Preliminaries
- 2.2 Multiply Transitive Groups
- 2.3 Regular Normal Subgroups and Multiple Transitivity
- 2.4 Sylow Theorems I
- 2.5 Sylow Theorems II
- 2.6 Nilpotent and Solvable Groups
- 3 Representations and Characters
- 3.1 Representations
- 3.2 Characters
- 3.3 Tensor Product of Two Matrices
- 3.4 Product of Two Characters
- 3.5 Induced Representations and Induced Characters
- 3.6 Burnside's paqb-theorem
- 4 Solvable Groups
- 4.1 Generalization of Sylow Theorems
- 4.2 Schur–Zassenhaus Theorem
- 5 Frobenius Groups
- 5.1 Introduction
- 5.2 Fixed-Point-Free Automorphisms
- 5.3 Characters of Some Finite Groups
- Appendix 1. Nonabelian Groups of Order pq (p > q are Prime Numbers)
- Appendix 2. Nonabelian Groups of Order p3, p an Odd Prime
- Appendix 3. A Group Having a Class Preserving Outer Automorphism
- Appendix 4. Outer Automorphism of S6
- Problems
- Hints or Solutions to Problems
- Glossary
- Credits and Sources Acknowledged
- Bibliography
- Index
