# Tour:Group of integers

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**This article adapts material from the main article:** group of integers

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WHAT YOU NEED TO DO: Read and understand the definition of the group of integers.

## Definition

### Usual definition

The **group of integers**, typically denoted , is defined as follows:

- The underlying set is the set of all integers
- The group operation is integer addition
- The identity element is the integer
- The inverse map is the additive inverse, sending an integer to the integer

In the 4-tuple notation, the group of integers in the group .

This page is part of the Groupprops guided tour for beginners. Make notes of any doubts, confusions or comments you have about this page before proceeding.PREVIOUS: Isomorphic groups|UP: Introduction four (beginners)|NEXT: Group of integers modulo nExpected time for this page: 2 minutes