Up to now, my main research has been about amalgams of groups, with particular emphasis special amalgams. The main tool I use are dominions (a notion developed by John Isbell), and I usually work in the context of varieties or pseudovarieties. The precise definitions are recalled in the next few pages.

   The general situation, at its most basic, is a very common one in mathematics. Say we have two objects of interest, G and K, and that they have a common subobject H. We want to "glue" the two objects along H to obtain a bigger object, M, which contains G and K as subobjects in such a way that their intersection, inside of M, equals H.

   In my case, the objects of interest are groups. The two groups G and K together with the specified common subgroup H is called an amalgam or group amalgam, and if we can find an M as above we say the amalgam can be (strongly) embedded (into M).

   The main question to ask is whether M exists or not; when we also have that G and K satisfy extra properties, we want to know whether M can be chosen to also satisfy them. Another way to think of this last point is to restrict our "objects of interest" from all groups to "all groups which satisfy such and such a property."

   In the rest of the introduction I will expand on some of the technical terms above and set the stage for a more precise description of the problem, as well as to describe its place in group theory in general.