Favorite Abelian groups?

[Abelian]

For me, it’s the Klein four group. It’s the smallest non-cyclic abelian group which gives it +10 aura.
its elements are (0,0) (0,1) (1,0) and (1,1) if
you think of it as the cross product of the integers mod 2

 

[Dagonet]

Huh?

 

[Abelian]

Huh?

a group is a mathematical object that consist of a set of elements that we call “members” of the group, as well as some operation that can combine group members together in a “nice” way (here, nice means that it is associative, invertible, and has an identity element)
an abelian group adds the extra rule that the group operation must be commutative; the order which you combine two elements doesn’t matter