Highgrove Education

Group Theory

Group Theory is the study of groups, which are mathematical structures with certain distinguishing properties; they also have numerous applications in Physics and Chemistry. In this elective, we will start by looking at the definition of a group, then see the relationship of groups to symmetries of shapes. Subgroups and their properties will be investigated, as well as particular types of groups called cyclic groups. We will explore the ideas of group isomorphisms, which are mappings between groups which preserve certain properties. We will then discuss cosets and their use in proving Lagrange’s theorem. Finally, we will look at normal subgroups and quotient groups.

Private Tuition

Key Information



Access Course Enrolment:
  • Enrolment in our pre-GCSE or pre-A level access course.
  • Access to our self-study materials and platform, live class lessons, and individual teacher support in Office Hours.
  • Weekly teacher-marked homework.
  • Half termly reports.
  • Support from our SENDCo for pupils with special educational needs or disabilities, including assessment for access arrangement entitlement.
  • Support with English for pupils whose first language is not English.
  • A Highgrove Education Office365 account, including Teams, SharePoint and a school email
TeacherDr Lampros Andrinopoulos, Physics and Mathematics Teacher
Course Length10 weeks 
Live LessonsOne 45-minute lesson per week
HomeworkApproximately half an hour a week 
Entry RequirementsPupils must be taking Mathematics or Further Mathematics at AS or A level, or pass an entry test to check their level of mathematics prior to joining this elective.

Course Syllabus

Lesson 1Group axioms
Lesson 2Modular arithmetic and groups; Cayley tables
Lesson 3Symmetries 
Lesson 4Rotation matrices and roots of unity as groups 
Lesson 5Subgroups, Lagrange's Theorem, cyclic groups 
Lesson 6Isomorphisms part I 
Lesson 7Isomorphisms part II 
Lesson 8Cosets, normal groups, quotient groups
Lesson 9Quotient groups; equivalence relations
Lesson 10Conjugacy and fixed point theorem

Teacher Profile

Dr Lampros Andrinopoulos studied a Master’s in Physics with Theoretical Physics at Imperial College London, where he also completed his PhD on dispersion interactions in density functional theory. He earned his teaching qualification (PGCE) in 2015 from Canterbury Christ Church University and has taught in a variety of schools since then, including Latymer, St Paul’s Girls’ School, and Harrow School Online.