Groups

Can you work out what simple structures have been dressed up in these advanced mathematical representations?

What groups of transformations map a regular pentagon to itself?

How many different transformations can you find made up from combinations of R, S and their inverses? Can you be sure that you have found them all?

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.

Explore the properties of some groups such as: The set of all real numbers excluding -1 together with the operation x*y = xy + x + y. Find the identity and the inverse of the element x.