On the efficiency of some finite groups

We describe a new technique for finding efficient presentations for finite groups. We use it to answer three previously unresolved questions about the efficiency of group and semigroup presentations.

Lorentz invariant intrinsic decoherence

We present a Lorentz invariant extension of a previous model for intrinsic decoherence (Milburn 1991 Phys. Rev. A 44 5401). The extension uses unital semigroup representations of space and time translations rather than the more usual unitary representation, and does the least violence to physically important invariance principles. Physical consequences include a modification of the uncertainty principle and a modification of field dispersion relations, similar to modifications suggested by quantum gravity and string theory, but without sacrificing Lorentz invariance. Some observational signatures are discussed.