  Pure three-qubit states have five algebraically independent and one
algebraically dependent polynomial invariants under local unitary
transformations and an arbitrary entanglement measure is a function of these
six invariants. It is shown that if the reduced density operator of a some
qubit is a multiple of the unit operator, than the geometric entanglement
measure of the pure three-qubit state is absolutely independent of the
polynomial invariants and is a constant for such tripartite states. Hence a
one-particle completely mixed state is a critical point for the geometric
measure of entanglement.
