Groups

Permutation groups of polynomial roots, dihedral and quaternion groups, Cayley tables, and group-property checks.

Galois’s permutation groups: S_3 permuting the roots of x^3 - 2

Galois's permutation groups: S_3 permuting the roots of x^3 - 2

Klein’s Erlangen program: the symmetry group of a square

Klein's Erlangen program: the symmetry group of a square

Hamilton’s quaternions: the group Q_8

Hamilton's quaternions: the group Q_8

Cayley’s abstract group and its multiplication table

Cayley's abstract group and its multiplication table