# Group Homomorphisms on the Integers Modulo n

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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 .

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