Contents

group theory

# Contents

## Idea

A finitely generated group is a (discrete) group (equipped) with a finite set of generators, hence of elements such that any other element can be written as a product of these.

## Properties

### Relation to Cayley graphs

Associated with a set of generators on a group is the corresponding Cayley graph, whose vertices are the group elements which are connected by an edge if they differ by (left, say) multiplication with one of the generators.

The corresponding graph distance equips the group with a metric (the word metric) and thus makes it an object of geometric group theory.

## Examples

###### Example

The symmetric group $Sym(n)$ may be generated from

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