Modern Algebra : Cyclic Groups

Definition of a Cyclic Group

The definition of a cyclic group is given along with several examples of cyclic groups.

 

Cyclic Subgroups

A definition of cyclic subgroups is provided along with a proof that they are, in fact, subgroups.

 

The Structure of Cyclic Groups

The following video looks at infinite cyclic groups and finite cyclic groups and examines the underlying structures of each. By looking at when the orders of elements in these groups are the same, several theorems are introduced and proven.

 

Cyclic Groups and Generators

What is a Cyclic Group/Subgroup? The following video give examples, theory, and proofs rounding off this topic.

 

Cyclic Groups and Abelian Groups

The following video explores the relationship between cyclic groups and abelian groups.