[Deprecated] Group Theory Lecture 6.2 Part 1 Orbit Stabilizer Theorem

We discuss the notion of orbits of a group action and that the orbits partition the entire set on which the group is acting. We then discuss the obit stabilizer theorem which connects the cardinality of the orbit of an element with the index of the stabilizer of that element, where the stabilizer of an element of the set is the set of all the group elements which leave the element fixed. We lastly discuss an application of the orbit stabilizer theorem by counting the size of the general linear group of a finite dimensional vector space over a finite field.

Keywords: Orbits, Actions, Groups, Stabilizer, General Linear Group, Finite Fields, Transitive Action.

00:00 Recap
03:22 Problems
03:53 Orbits
08:52 Orbits via an Equivalence Relation
14:12 Transitive Action
18:54 Orbit Stabilizer Theorem
24:56 An Application of OST

Note: The auto-generated subtitles are mostly accurate and may enhance experience.

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