Pronunciation: /grup/ Explain
A group is a
defined on members of that set. The operation must meet the requirements of
Example: the set of real numbers under addition is a group since:
- Closure: for any real numbers a and b, a + b = c if and only if c is a real number.
- Associativity: for any real numbers a, b and c, a+(b+c) = (a+b)+c.
- Identity: 0 is the additive identity for real numbers because for any real number a, a + 0 = a and 0 + a = a.
- Invertibility: for every real number a, there is an additive inverse -a such that a + (-a) = 0.
A commutative group is a
group where the operation is also
If, for any members of the group S, a and b, a*b = b*a, then group S
is a commutative group. Commutative groups are also called
- McAdams, David E.. All Math Words Dictionary, group. 2nd Classroom edition 20150108-4799968. pg 88. Life is a Story Problem LLC. January 8, 2015. Buy the book
Cite this article as:
McAdams, David E. Group. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/g/group.html.
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/10/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
5/5/2011: Initial version. (McAdams, David E.)