Cyclic Group C_11

The cyclic group C_(11) is unique group of group order 11. An example is the integers modulo 11 under addition (Z_(11)). No modulo multiplication group is isomorphic to C_(11). Like all cyclic groups, C_(11) is Abelian.


The cycle graph of C_(11) is shown above. The cycle index is


Its multiplication table is illustrated above.

Because the group is Abelian, each element is in its own conjugacy class. Because it is of prime order, the only subgroups are the trivial group and entire group. C_(11) 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 C4, Cyclic Group C5, Cyclic Group C6, Cyclic Group C7, Cyclic Group C8, Cyclic Group C9, Cyclic Group C10, Cyclic Group C12

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Cite this as:

Weisstein, Eric W. "Cyclic Group C_11." From MathWorld--A Wolfram Web Resource.

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