After studying this course, you should be able to:
apply the Internal Direct Product Theorem in simple cases
decide whether a given group is cyclic, and given a finite cyclic group, find a generator for a subgroup of a given order
express a given finite cyclic group as the direct product of cyclic groups of prime power order and, given two direct products of cyclic groups, determine whether or not they are isomorphic
express products of elements of a group defined by generators and relations in appropriate standard form
recognise the dihedral and dicyclic groups when described using a standard form.