Widget wrote:

Could someone give some examples of the what this example means?

"Relations among abstract structures of mathematical operations (e.g., detecting structural isomorphisms between groups of mathematical operations in disparate structures of mathematical operations ."

this is from a developmental psychology textbook under

Table 6.1 Developmental Transformations of Hierarchical Complexity in Three Domains
Group isomoprhism: A one to one onto mapping from group G to group G' that preserves group structure. Let h be such an isomorphism. then for x, y in G and where * is the group operator h(x*y) = h(x)*'h(y) where *' the group operator of G'.

h(x inverse) = h(x) inverse and h(identity element of G) is the identity element of G'

A homomorphism is like an isomorphism except h has to be a mapping from G onto G'. It need not be one to one

For more one Groups see any book on abstract algebra. Examples of groups: The real numbers where +is the operation and 0 is the identity element.