# Tour:Trivial group

From Groupprops

**This article adapts material from the main article:** trivial group

This page is part of the Groupprops guided tour for beginners (Jump to beginning of tour)PREVIOUS: Subgroup|UP: Introduction one (beginners)|NEXT: Verifying the group axiomsExpected time for this page: 1 minute

General instructions for the tour | Pedagogical notes for the tour | Pedagogical notes for this part

WHAT YOU NEED TO DO:

- Understand the definition of trivial group given below
- Convince yourself that this is indeed a group

## Definition

### Verbal definition

The **trivial group** is the group with only one element, which is its identity element. The trivial group is usually denoted as , , or .

[SHOW MORE]PONDER (WILL BE EXPLORED LATER IN THE TOUR):

- Over why the trivial group occurs as a subgroup in any group
- Over why the trivial group is Abelian
WHAT'S MORE: Some alternative descriptions, and important facts, about the trivial group. Ignore the parts that use terminology you haven't encountered so far.