  We study the relationship between Bell states, finite groups and complete
sets of bases. We show how to obtain a set of N+1 bases in which Bell states
are invariant.
  They generalize the X, Y and Z qubit bases and are associated to groups of
unitary transformations that generalize the sigma operators of Pauli. When the
dimension N is a prime power, we derive (in agreement with well-known results)
a set of mutually unbiased bases. We show how they can be expressed in terms of
the (operations of the) associated finite field of N elements.
