Learning outcomes

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.