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Examples of Abelian Groups

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group
{4,3,3,3}
view
2D
3D
Cayley graph
In an Abelian group, the elements commute:
AB=BA
for any elements
A
and
B
in the group. Therefore, the multiplication table of an Abelian group is symmetric, and plotting the resulting pattern can reveal interesting structures. The index
{
n
1
,
n
2
,…}
represents the direct product of the cyclic groups
C
n
1
⊗
C
n
2
⊗…
. The Cayley graph encodes how the products of the group generators produce all the elements of the group (mouse over the vertices). A selection is shown because some examples are trivial, some combinations are not allowed, and tables grow arbitrarily large.
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