Tour:Trivial group

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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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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 1, \{ 1 \}, or \{ e \}.

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.
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