String numbers of abelian groups

Details String numbers of abelian groups String numbers of abelian groups

2010-06-27

arxiv.org/abs/1006.5206v3

Mathematics

Group Theory

22 pages

Scientific paper

The string number of self-maps arose in the context of algebraic entropy and it can be viewed as a kind of combinatorial entropy function. Later on its values for endomorphisms of abelian groups were calculated in full generality. We study its global version for abelian groups, providing several examples involving also Hopfian abelian groups. Moreover, we characterize the class of all abelian groups with string number zero in many cases and discuss its stability properties.

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