Abstract Algebra - 1.2 Cayley Tables and an Introduction to Groups

We further develop our understanding of the symmetries of a square by constructing both a Cayley diagram and Cayley table (multiplication table). We also briefly discuss why the symmetries form a group, though we will leave the official definition of a group to video 2.1.

Video Chapters:
Intro 0:00
Recap the Symmetries of Square 0:12
Recap of Composition of Actions 4:37
Intro to Cayley Diagrams (not in textbook) 6:46
Our First Cayley Table 10:43
What Makes This a Group? 20:36
Up Next 23:07

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

[xoppa]

@10:21 It appears that the labels in the diagram is clashing with composition 'right to left' notation convention.
For example the arrow from r to f on the left (at the 9 aclock position) should give us the node "fr" instead of " rf", since we read composition of actions from right to left.
Another way of saying this is that arrows should act on the left.

[mehularora]

Finally some group theory! Thanks for the awesome content

[ahasdasetodu]

The inconsistency of notation in this video makes it hard to watch, I feel like reading transformations right to left makes sense but what doesnt is the fact that depending on the context it's read left to right or right to left. Pick one way of reading and stick to it instead of introducing so much unnecessary chaos.
Edit: Just got to the part where (rf)(r^3) is calculated which is completely wrong, or rather the answer is right for the wrong reasons. In this equation the compostition notation is being used for the first part (doing r^3) but when it comes to rf insted of doing f first then r which would land us in r^2f it does the opposite. A much cleaner way to write this would be (r^3)(rf) and then from associativity it becomes (r^3r)f=ef=f

[jiahao]

a lot mistake, the writing is not consistent...