  Given a finite group G with a bilocal representation, we investigate the
bipartite entanglement in the state constructed from the group algebra of G
acting on a separable reference state. We find an upper bound for the von
Neumann entropy for a bipartition (A,B) of a quantum system and conditions to
saturate it. We show that these states can be interpreted as ground states of
generic Hamiltonians or as the physical states in a quantum gauge theory and
that under specific conditions their geometric entropy satisfies the entropic
area law. If G is a group of spin flips acting on a set of qubits, these states
are locally equivalent to 2-colorable (i.e., bipartite) graph states and they
include GHZ, cluster states etc. Examples include an application to qudits and
a calculation of the n-tangle for 2-colorable graph states.
