Cyclic group
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A cyclic group is a group that can be generated by repeatedly applying the group operation to a single element. Every member of the group is a power or integer multiple of that generator, depending on the notation used.
Finite cyclic groups have a fixed number of elements and are isomorphic to the integers modulo that number under addition. Infinite cyclic groups are isomorphic to the ordinary integers under addition.
Every cyclic group is abelian because the order of combining its elements does not affect the result. A cyclic group may have several different generators.
Cyclic groups are among the simplest structures in abstract algebra. They appear in number theory, symmetry, modular arithmetic, cryptography, rotations, and the classification of more complicated groups.
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- Source / publisher: Wikipedia
- URL type: WWW
- Credits: Wikipedia
- URL: https://en.wikipedia.org/wiki/Cyclic_group