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)
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WHAT YOU NEED TO DO:
- Understand the definition of trivial group given below
- Convince yourself that this is indeed a group
The trivial group is the group with only one element, which is its identity element. The trivial group is usually denoted as , , or .
PONDER (WILL BE EXPLORED LATER IN THE TOUR):[SHOW MORE]
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.
- Over why the trivial group occurs as a subgroup in any group
- Over why the trivial group is Abelian