Sunday, September 9, 2012

Iteration classes

The relation between iterates is an equivalence relation. The equivalence classes of this relation are called iteration classes. Non-iterable functions, involutions, and reductions all have a single distinct iteration element so their iteration classes are trivial.

Cycles can be reduced to iterations of an element whose first two elements are minimal. On the other hand, finite automorphisms that have different orders are iterates of one another if the element with the larger order can be iterated by its own order divided by the order of the other element to get the other element.

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