Groups and Group Actions: Representations of groups by permutations - 1st Year Student Lecture

From Oxford Mathematics

In this lecture from the Groups and Group Actions first year course, Nikolay Nikolov shows that every group action gives rise to a homomorphism into some group of permutations. As an application we prove Cayley's theorem (stating that every finite group is isomorphic to a subgroup of some symmetric group), and we determine the rotation groups of regular polyhedra. You can watch other lectures from the course: https://www.youtube.com/playlist?list=PL4d5ZtfQonW2HoddSQU2V9XTtRl6iN88U You can wat...