Part: Group Theory

In this part, we dive deeper into the theory of groups.

Examples: 1

  1. Definition: Generating Set of a Group
  2. Definition: Group Homomorphism
  3. Proposition: Additive Subgroups of Integers
  4. Theorem: Construction of Groups from Commutative and Cancellative Semigroups
  5. Definition: Cyclic Group, Order of an Element
  6. Proposition: Finite Order of an Element Equals Order Of Generated Group
  7. Proposition: Group Homomorphisms with Cyclic Groups
  8. Lemma: Cyclic Groups are Abelian
  9. Lemma: Subgroups of Cyclic Groups
  10. Proposition: Subgroups of Finite Cyclic Groups
  11. Definition: Direct Product of Groups
  12. Definition: Conjugate Elements of a Group
  13. Definition: Cosets
  14. Proposition: Properties of Cosets
  15. Lemma: Subgroups and Their Cosets are Equipotent
  16. Theorem: Order of Subgroup Divides Order of Finite Group
  17. Theorem: Order of Cyclic Group (Fermat's Little Theorem)
  18. Chapter: Symmetry Groups
  19. Definition: Normal Subgroups
  20. Lemma: Factor Groups
  21. Lemma: Group Homomorphisms and Normal Subgroups
  22. Theorem: First Isomorphism Theorem for Groups
  23. Theorem: Classification of Cyclic Groups
  24. Theorem: Classification of Finite Groups with the Order of a Prime Number
  25. Definition: Group Operation

Branches: 1
Explanations: 2

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