Abstract Algebra - 6.1 Definition and Understanding of Isomorphisms

In this video we will introduce the concept of an isomorphism by comparing the group D4, the symmetries of a square, to a permutation group. We will examine the mapping of elements of one group to the other, as well as verifying the properties of one-to-one, onto and operation-preserving.

We will also look at a second example that cannot be modeled using a Cayley diagram.

Video Chapters:
Intro 0:00
What is an Isomorphism 0:16
Relabeling a Cayley Diagram 5:20
Definition of an Isomorphism 7:50
D4 Isomorphic to a subgroup of S4 11:52
Prove (R,+) is Isomorphic or (R+, X) 15:43
Up Next 20:31

This playlist follows Gallian text, Contemporary Abstract Algebra, 9e.

[Mesohornet]

For rf why do we go r then f at 4:10, giving (14)(23). I thought rf mean f then r, which would give (12)(34). Do you do left first multiplication in your class? Also do you do cycle multiplication right to left? Thanks!

[elyrr]

help, how to find the possible values for φ(ρ) and φ(μ) to produce an isomorphism φ: D3 → S if set S={1/x, 1/(1-x), (x-1)/x, x/(x-1), x, (1-x)} and D3 = {e, ρ, ρ^2, μ, μρ, μρ^2}.

[kenmeyer]

Kimberly, did you intentionally leave out videos for chapters 3 to 5 or aren't there any?