Pathway VII

⋆Algebraic structures and transformations

Magmas, groups, homomorphisms — a set with an operation, and the maps that preserve it.

1. 01GroupsA group is a set with an associative operation, identities, and inverses. Cyclic groups are clocks.4 min
2. 02HomomorphismsA homomorphism is a map that preserves the operation. Kernels are the stuff sent to the identity.4 min
3. 03Group actionsA group transforms a set. Orbits partition the set; stabilizers are the symmetries of a point.4 min