String numbers of Abelian groups. (Q2909813)
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scientific article; zbMATH DE number 6078491
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | String numbers of Abelian groups. |
scientific article; zbMATH DE number 6078491 |
Statements
6 September 2012
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torsion-free Abelian groups
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hereditarily Hopfian groups
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string numbers
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powers of endomorphisms
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String numbers of Abelian groups. (English)
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A string in an Abelian group is the trajectory of an element under the powers of an endomorphism of the group; and a string number is a statistic concerning the size of certain families of disjoint strings that the group admits as the endomorphism varies.NEWLINENEWLINE The authors study several examples, demonstrate the relationship between string numbers and algebraic entropy, and prove a surprising connection with the theory of Hopfian groups.
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