An excerpt from my lecture notes on relativity (translated from Dutch):
"Special (special in the notes indicates that the determinant of the representation matrix equals +1) Lorentz transformations with arbitrary velocities don't form a group. Special Lorentz transformations form a group (an Abelian subgroup of the Lorentzgroup) only when the boosts are parallel."
I don't see this. Why don't arbitrary boosts in arbitrary directions form a group? What criterion (closed under the operation, existence of the inverse, containing neutral element etc) of forming a group is not satisfied here?