This article only skims the surface of Galois theory and should
probably be accessible to a 17 or 18 year old school student with a
strong interest in mathematics.
The binary operation * for combining sets is defined as the union
of two sets minus their intersection. Prove the set of all subsets
of a set S together with the binary operation * forms a group.
An environment for exploring the properties of small groups.
A group is a set of elements together with a binary operation (which we denote here by $*$) with the following properties:
Some groups, which are called COMMUTATIVE or ABELIAN, have the property that, for all pairs of elements in the group, $a*b=b*a$.