What is an Abelian group, from a linear/abstract algebra perspective?
1 Answer
An Abelian group is a group with the additional property of the group operation being commutative.
Explanation:
A group

#G# is closed under#•# .
For any#a,binG# , we have#a•b in G# 
#•# is associative.
For any#a,b,cinG# , we have#(a•b) • (c) = a •(b•c)# 
#G# contains an identity element
There exists#einG# such that for all#ainG# ,#a•e=e•a=a# 
Each element of
#G# has an inverse in#G#
For all#ainG# there exists#a^(1)inG# such that#a•a^(1)=a^(1)•a=e#
A group is said to be Abelian if it also has the property that
The group
The group
but