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

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 watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists): https://www.youtube.com/playlist?list=PL4d5ZtfQonW0A4VHeiY0gSkX1QEraaacE All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.