This work demonstrates self-similar structures in free abelian groups of uncountable rank, indicating significant properties of infinite products.
In this work we study the self-similarity of infinite products of the group of the integers. In [6], the authors ask if there is a self-similar free abelian group of uncountable rank. On the other hand, in [3] is asked if the Baer-Specker group ℤ 𝜔 is self-similar (by a result of R. Baer, this group is not free abelian). We answer both questions positively.
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Dantas et al. (2026) studied this question.
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