# Abstract Algebra: Groups

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• Mar 4th 2008, 11:30 PM
Jhevon
Abstract Algebra: Groups
Hi all,

A general, and perhaps stupid, question: Can we have a group with one element? If so, what's an example?

Thanks all :D

EDIT: could a group with a single element and the identity function as the operation work?
• Mar 5th 2008, 03:13 AM
mr fantastic
Quote:

Originally Posted by Jhevon
Hi all,

A general, and perhaps stupid, question: Can we have a group with one element? If so, what's an example?

Thanks all :D

EDIT: could a group with a single element and the identity function as the operation work?

Yes. I quote from Group (mathematics) - Wikipedia, the free encyclopedia:

"A trivial group is a group consisting of a single element. All such groups are isomorphic so one often speaks of the trivial group. The single element of the trivial group, variously labeled e, 1, or 0, is the identity element. The group operation is e + e = e."

See also Trivial Group -- from Wolfram MathWorld