5 July 2021

Over the last term, the Cartwright Group has been delving into the undergraduate world of Group Theory, looking for abstract patterns in various contexts including modular arithmetic, transformations of shapes, complex numbers and ways to put on a T-Shirt in the dark. This culminated with constructing the Cayley Table for the group S4, which are all the possible symmetries of the tetrahedron, and how they combine together, before finding some of the subgroups and comparing them to earlier finds – Klein 4, C3, C4, C2 and a few new groups – S3, D8 and A4.

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