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First-Semester Abstract Algebra: A Structural Approach
This text is specifically designed to suit a single-semester introductory abstract course, rather than to be a comprehensive reference source.
- Author
- Jessica K. Sklar
- Publisher
- Pacific Lutheran University
- Source
- LibreTexts
- License
- GNU FDL
- Language
- EN
- Category
- Basic Sciences
Contents· 48 sections
- 01: Preliminaries
- 1.01: Sets
- 1.02: Functions
- 1.03: Cardinality
- 1.04: Exercises
- 02: Groups
- 2.01: Binary Operations and Structures
- 2.02: Exercises, Part I
- 2.03: The Definition of a Group
- Nongroups, Part I
- 2.05: Group Conventions and Properties
- Nongroups, Part II
- 2.07: Summaries of Groups We've Seen
- 2.08: Exercises, Part II
- 03: Homomorphisms and Isomorphisms
- 3.01: Groups of Small Order
- 3.02: Definitions of Homomorphisms and Isomorphisms
- 3.03: Isomorphic Groups
- 3.04: Exercises
- 04: Subgroups
- 4.01: Introduction to Subgroups
- 4.02: Subgroup Proofs and Lattices
- 4.03: Exercises
- 05: Cyclic Groups
- 5.01: Introduction to Cyclic Groups
- 5.02: The Subgroup Lattices of Cyclic Groups
- 5.03: Exercises
- 06: Permutation and Dihedral Groups
- 6.01: Introduction to Permutation Groups
- 6.02: Symmetric Groups
- 6.03: Alternating Groups
- 6.04: Cayley's Theorem
- 6.05: Dihedral Groups
- 6.06: Exercises
- 07: The Wonderful World of Cosets
- 7.01: Partitions of and Equivalence Relations on Sets
- 7.02: Introduction to Cosets and Normal Subgroups
- 7.03: The Index of a Subgroup and Lagrange's Theorem
- 7.04: Exercises
- 08: Factor Groups
- 8.01: Motivation
- 8.02: Focusing on Normal Subgroups
- 8.03: Introduction to Factor Groups
- 8.4: Exercises
- 09: The Isomorphism Theorem
- 9.01: The First Isomorphism Theorem
- 9.02: The Second and Third Isomorphism Theorems
- 9.03: Exercises