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Math 2.0

Group theory and generalizations Example

Trivial group

Example

The trivial group is the group $\{e\}$ with one element $e$ and the operation $e \cdot e = e$ . The element $e$ is the identity element, and it is its own inverse. Each group with exactly one element is isomorphic to this group.

Remarks

Each group $G$ contains a trivial subgroup $\{e\}$ , where $e$ is the identity of $G$ . In additive notation the trivial group is written $0$ or $\{0\}$ . The trivial group is abelian, and its order is $1$ .

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Zero object

Further reading

Web https://en.wikipedia.org/wiki/Trivial_group, lead section

About this page

Tag	`0BNPC9850Y`
URI	`m2://0BNPC9850Y`
Aliases	`zero-group`
Kind	example
Writing	W2 usable
MSC	20A05
Instance of	Group
Same as	Wikidata Q568687 Wikipedia Trivial group

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Zero object