My OpenLearn Profile
Personalise your OpenLearn profile, save your favourite content and get recognition for your learning
Group theory
This free course consolidates and builds on group theory studied at OU level 2 or equivalent. Section 1 describes how to construct a group called the direct product of two given groups, and then describes certain conditions under which a group can be regarded as the direct product of its subgroups. Section 2 describes the key properties of the structure of cyclic groups. Section 3 introduces the notion of a set of generators of a group and a set of relations among the generators. It then looks at a family of finite groups, the dicyclic groups.
Course 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.
First Published: 09/03/2018
Updated: 07/12/2018
Rate and Review
Create an account to get more
Track your progress
Review and track your learning through your OpenLearn Profile.
Statement of Participation
On completion of a course you will earn a Statement of Participation.
Access all course activities
Take course quizzes and access all learning.
Review the course
When you have finished a course leave a review and tell others what you think.
very bad better not in a PDF fille and need more tested on line and atvives .