Proof & Example: Orbit-Stabilizer Theorem - Group Theory

The orbit stabilizer theorem is a very important theorem about group actions. In this video we give an intuitive explanation of the orbit stabilizer theorem and an example with the symmetric group!

0:00 Stabilizer is a subgroup
3:26 Orbit-stabilizer theorem
12:23 Example

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Music: C418 - Pr Department

[MuPrimeMath]

For anyone interested, when two group actions of G "work the same way", we say that the two are *isomorphic as G-sets* . That idea gives us a more specific way of thinking about the similarity of group actions!

[joetursi]

I just looked at this again and I think it's better than any other attempt at the Orbit-Stab theorem. Step by step, it's easy to understand .

[이재헌-eo]

all of your lectures helped me a lot!! I wish my prof could explain as simply as you do. You explained where things came from and what they mean. Thank you a lot!!

[ethanjensen]

I'm learning modular forms, but I haven't had the chance to take Abstract Algebra at my university yet. This video was super stimulating and useful. Thank you.

[albertyeung]

Not many people talk about this thm in their introduction to Group Theory

[sanelprtenjaca]

I just started to learn abstract algebra but your explanations are smooth enough for me to understand most of this!

[hiranabe]

Great explanation!! thanks a lot. i'm tempted to explain Lagrange thm as a consequence of Orbit-Stabilizer thm, using left product as an action. are you?

[andrewgraybar]

Perhaps gather 300 of these presentations, and self-publish a textbook.
And, for each one, a page alongside stating the most frequent applications, or uses in industry, or
Uses by actuaries, or suggestions for usage. Then, when a potential employer asks for your resume
(C.V., if you wish), you hand them the textbook. How cool is that. Pop

[jabir]

Doing a lot of online classes made me realise how hard it is to explain things properly, you're really good at explaining, keep it up!