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There are **11** NRICH Mathematical resources connected to **Groups**, you may find related items under Patterns, sequences and structure.

Problem
Primary curriculum
Secondary curriculum
### Sheep in Wolf's Clothing

Can you work out what simple structures have been dressed up in these advanced mathematical representations?

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Paint Rollers for Frieze Patterns.

Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.

Age 11 to 16

Article
Primary curriculum
Secondary curriculum
### Dancing with Maths

An article for students and teachers on symmetry and square dancing. What do the symmetries of the square have to do with a dos-e-dos or a swing? Find out more?

Age 7 to 16

Article
Primary curriculum
Secondary curriculum
### Grouping Transformations

An introduction to groups using transformations, following on from the October 2006 Stage 3 problems.

Age 11 to 18

Problem
Primary curriculum
Secondary curriculum
### Simplifying Transformations

How many different transformations can you find made up from combinations of R, S and their inverses? Can you be sure that you have found them all?

Age 11 to 14

Challenge Level

Article
Primary curriculum
Secondary curriculum
### An Introduction to Mathematical Structure

An introduction to the sort of algebra studied at university, focussing on groups.

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Groups of Sets

The binary operation * for combining sets is defined as the union of two sets minus their intersection. Prove the set of all subsets of a set S together with the binary operation * forms a group.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's a Group?

Explore the properties of some groups such as: The set of all real numbers excluding -1 together with the operation x*y = xy + x + y. Find the identity and the inverse of the element x.

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### An Introduction to Galois Theory

This article only skims the surface of Galois theory and should probably be accessible to a 17 or 18 year old school student with a strong interest in mathematics.

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### Small Groups

Learn about the rules for a group and the different groups of 4 elements by doing some simple puzzles.

Age 16 to 18