A β-ring is supplied with operations βH
where H runs over the conjugacy classes
of subgroups of the symmetric groups Sn. In
earlier paper we introduced a second
set of operations λH and we show here that the
two sets are related by the isomorphism
We then consider the operations βH and
λH as combinatorial species, in the sense of
Joyal, and express their molecular decomposition as a finite sum of
products of the
exponential species with molecular species of degree at most n.
We give combinatorial
interpretations for βSn-structures
and derive various species isomorphisms.