Topics in Finite Groups

Inbunden, Engelska, 2021

Av Gail Gallitano, Shiv Gupta, Gallitano Gail, Gupta Shiv

6 999 kr

Slutsåld

Topics in Finite Groups introduces the basic concepts of Group Theory and is rich in illustrative examples which will help the readers to understand and appreciate this beautiful area of mathematics. The topics discussed include Permutation Groups and Sylow Theorems, Representation and Characters, Solvable Groups, Frobenius Groups. Over one hundred problems of varying degrees of difficulty along with their partial or complete solutions are included.

Produktinformation

Utgivningsdatum2021-08-18
FormatInbunden
SpråkEngelska
FörlagKendall/Hunt Publishing Co ,U.S.
ISBN9781792480003

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Matematik inom Naturvetenskap och teknik

1 Introduction 1.1 Preliminary Definitions1.2 Examples of Groups1.3 Some Basic Group Concepts and Terminology1.4 Cyclic Groups1.5 Direct and Semidirect Product of Groups1.5.1 Direct Product1.5.2 Examples of Direct Product1.5.3 Semidirect Product1.5.4 Examples of Semidirect Product1.6 Isomorphism, Homomorphism, and Automorphism1.6.1 Isomorphism and Homomorphism1.6.2 Examples of Isomorphic Groups1.6.3 Homomorphism and Kernel of Homomorphism1.6.4 Examples of Quotient Groups1.6.5 Homomorphism/Isomorphism Theorems1.6.6 Abelian p-groups1.6.7 Composition Series of Finite Groups1.6.8 Jordan–Hölder Theorem1.6.9 Automorphism group of a group1.6.10 The Group Z?n2 Permutation Groups and Sylow Theorems 2.1 Preliminaries2.2 Multiply Transitive Groups2.3 Regular Normal Subgroups and Multiple Transitivity2.4 Sylow Theorems I2.5 Sylow Theorems II2.6 Nilpotent and Solvable Groups3 Representations and Characters 3.1 Representations3.2 Characters3.3 Tensor Product of Two Matrices3.4 Product of Two Characters3.5 Induced Representations and Induced Characters3.6 Burnside's paqb-theorem4 Solvable Groups 4.1 Generalization of Sylow Theorems4.2 Schur–Zassenhaus Theorem5 Frobenius Groups 5.1 Introduction5.2 Fixed-Point-Free Automorphisms5.3 Characters of Some Finite GroupsAppendix 1. Nonabelian Groups of Order pq (p > q are Prime Numbers)Appendix 2. Nonabelian Groups of Order p3, p an Odd PrimeAppendix 3. A Group Having a Class Preserving Outer AutomorphismAppendix 4. Outer Automorphism of S6 ProblemsHints or Solutions to ProblemsGlossaryCredits and Sources AcknowledgedBibliographyIndex

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