your next task is to provide the mathematical group structure (as defined at the beginning of this (25) section) to the set of all bijections of a given set. the group interface is the same as the previous assignment, reproduced below: public interface group { /** * performs the binary operation, as defined by the group, of one object with the other specified * object. the implementer must take care to ensure that the binary operation is *

• * * * * * * * * * * * * * *

* closed for the parameter type t. that is, the result of the binary operation is a valid member of the set that defines the type t (taking the denotational semantics view of data types). for example, addition is a binary operation that is closed for integers, but division is not. associative. that is, for any elements x, y, and z in this group, binaryoperation(binaryoperation(x, y), z) is equal to binaryoperation(x, binaryoperation(y, z)). for example, addition is an associative binary operation for integers. respectful of the identity element. that is, for any element x in this group and the identity element e of this group, binaryoperation(x, e) is equal to x, and binaryoperation(e, x) is also equal to x. for exam