Difference between revisions of "Abelian group"
Pi3point14 (talk | contribs) |
Pi3point14 (talk | contribs) |
||
Line 10: | Line 10: | ||
Inverse Element | Inverse Element | ||
For all <math>a \in S</math>, there exists some <math>a^{-1}</math> such that <math>a \bullet a^{-1} = e</math> | For all <math>a \in S</math>, there exists some <math>a^{-1}</math> such that <math>a \bullet a^{-1} = e</math> | ||
− | + | Commutativity | |
+ | For all <math>a,b \in S</math>, <math>a \bullet b = b \bullet a</math>. | ||
{{stub}} | {{stub}} |
Revision as of 18:42, 12 August 2015
An abelian group is a group in which the group operation is commutative. For a group to be considered "abelian", it must meet several requirements.
Closure
For all![]()
![]()
, and for all operations
,
.
Associativity
For all![]()
![]()
and all operations
,
.
Identity Element
There exists somesuch that
.
Inverse Element
For all, there exists some
such that
![]()
Commutativity
For all,
.
This article is a stub. Help us out by expanding it.