When I'm studying, I often find myself searching for the minimal conditions to define something. A simple example is: to define a circumference in a plane you need 3 points or 1 point and a distance, or even 4 points, but this last one is not "efficient" (also, not all 4 sets of points define a circumference).
This way of thinking can also be applied to other concepts like specific algebras, that is my main focus. For example, what is the minimum conditions needed to define a group.
I was wondering, is there a math field that studies this kinds of problems?
Thank you for your help.