The study of symmetry. A group is a set with an operation (like addition) that follows specific rules: it must be associative, have an identity element (like zero), and every element must have an inverse.
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These add a second operation (multiplication) to the group structure. Examples include integers or polynomials. They help us understand how different types of "numbers" behave when you both add and multiply them. The study of symmetry
by Charles Pinter (Available very cheaply or through many university libraries). To help you get the exact material you need: The specific edition or author (if not Gilbert & Gilbert) have an identity element (like zero)