Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

The group consists of the residue classes of the integers modulo under addition. This Demonstration illustrates the action of a group homomorphism . Such a mapping must have the form for some in . The homomorphism is an automorphism if and only if is a generator of the cyclic group .

Contributed by: Marc Brodie (June 2020)

(Benedictine University Mesa)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The operation for an Abelian group is typically written as addition. A group homomorphism is a mapping from a group to a group such that for all and in . The kernel of a homomorphism consists of those elements in whose image is the identity in . An isomorphism is a one-to-one homomorphism from onto . An automorphism of a group is an isomorphism .

## Permanent Citation