is the unique group
of group order 5, which is Abelian.
Examples include the point group and the integers mod 5 under addition ( ). No modulo multiplication
group is isomorphic to .
cycle graph is shown above, and the cycle
where 1 is the identity element.
multiplication table is illustrated above
and enumerated below.
is Abelian, the conjugacy classes are , , , , and . Since 5 is prime, there are no subgroups except the trivial
group and the entire group. is therefore a simple group,
as are all cyclic graphs of prime order.
See also Cyclic Group
Cyclic Group C2
Cyclic Group C3
Cyclic Group C6
Cyclic Group C8
Cyclic Group C10
Cyclic Group C12
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Cite this as:
Weisstein, Eric W. "Cyclic Group C_5."
From --A Wolfram Web Resource. MathWorld https://mathworld.wolfram.com/CyclicGroupC5.html