Cyclic Groups, Generators, and Cyclic Subgroups | Abstract Algebra

We introduce cyclic groups, generators of cyclic groups, and cyclic subgroups. We discuss an isomorphism from finite cyclic groups to the integers mod n, as well as an isomorphism from infinite cyclic groups to the integers. We establish a cyclic group of order n is isomorphic to Zn, and an infinite cyclic group is isomorphic to the integers. Finally, we introduce cyclic subgroups, and show the powers of an element will always form a cyclic subgroup. #abstractalgebra #grouptheory

Every Cyclic Group is Abelian:    • Every Cyclic Group is Abelian | Abstr...  
Every Subgroup of a Cyclic Group is Cyclic:    • Every Subgroup of a Cyclic Group is C...  
A Cyclic Group of Permutations:    • A Cyclic Group of Permutations | Abst...  

Abstract Algebra Course:    • Abstract Algebra  
Abstract Algebra Exercises:

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