Periods of endomorphisms on an Abelian group (Q2850660)
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scientific article; zbMATH DE number 6212864
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Periods of endomorphisms on an Abelian group |
scientific article; zbMATH DE number 6212864 |
Statements
27 September 2013
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periodic point
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group endomorphism
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Periods of endomorphisms on an Abelian group (English)
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Associated to any map \(f:X\to X\) is the set of periods, comprising those integers \(n\) with the property that some \(x\in X\) has a periodic orbit of length \(n\) under iteration of \(f\). Here it is shown that a set of integers is the set of periods for an endomorphism of an abelian group if and only if it contains \(1\) and is closed under taking least common multiples.
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