  In this work, we study generalized entropies and information geometry in a
group-theoretical framework. We explore the conditions that ensure the
existence of some natural properties and at the same time of a
group-theoretical structure for a large class of entropies. In addition, a
method for defining new entropies, using previously known ones with some
desired group-theoretical properties is proposed. In the second part of this
work, the information geometrical counterpart of the previous construction is
examined and a general class of divergences are proposed and studied. Finally,
a method of constructing new divergences from known ones is discussed; in
particular, some results concerning the Riemannian structure associated with
the class of divergences under investigation are formulated.
