Concrete self-similar representations of some subgroups of the Baer–Specker group

International Journal of Algebra and Computation 2026

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Authors: Alex C. Dantas, Jean Lelis, Bruno Zaban
DOI: 10.1142/s0218196726500244
Cited by: 0
References: 9

Abstract

In this work we study the self-similarity of infinite products of the group of the integers. In [A. C. Dantas, T. M. G. Santos and S. N. Sidki, Self-similar abelian groups and their centralizers, Groups Geom. Dyn. 17 (2023) 1–23], the authors ask if there is a self-similar free abelian group of uncountable rank. On the other hand, in [L. Bartholdi and S. N. Sidki, Self-similar products of groups, Groups Geom. Dyn. 14(1) (2020) 107–115] is asked if the Baer–Specker group [Formula: see text] is self-similar (by a result of R. Baer, this group is not free abelian). We answer both questions positively.

Fields of Study & Subjects

Finite Group Theory Research Mathematical Dynamics and Fractals Geometric and Algebraic Topology

Publication details

Journal / source
International Journal of Algebra and Computation
Volume
36
Issue
06
Pages
693–701
Publication date
6 March 2026
Language
EN