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Constructs many non-embeddable torsion-free groups with varying cardinalities, highlighting their complexity.
In an elementary way, we construct a family of pairwise non-embeddable torsion-free groups which contains <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mn>2</m:mn> <m:mi>κ</m:mi> </m:msup> </m:math> 2κ groups of cardinality 𝜅 for every infinite cardinal number 𝜅 up to the first strong limit cardinal of uncountable cofinality.
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Gerald Kuba (2026) studied this question.
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