Let us set aside for the moment the amalgams and discuss the seemingly unrelated concept of equalizers. If you will bear with me, I will connect it with amalgams in the next section.

   Say you have two morphisms of groups with the same domain and range, f,g:G->K. The equalizer of f and g, Eq(f,g), is the subgroup of G of all elements x such that f(x)=g(x).

   A subgroup of G which equals the equalizer of a pair of maps is called an equalizer subgroup.

   If we are dealing only with groups in a particular class C, then we are interested in knowing general properties about equalizer subgroups. As a somewhat trivial example, if we restrict the groups K (but not the groups G) to the class of abelian groups, then every equalizer subgroup contains the commutator subgroup of G.

   Note that if both f and g are injective, then the special amalgam of G with itself over Eq(f,g) is strongly embeddable, into K, via f and g.