Affiliation:
1. Department of Mathematics , Vanderbilt University , Nashville 37240 , USA
Abstract
Abstract
A finitely generated group 𝐺 is said to be condensed if its isomorphism class in the space of finitely generated marked groups has no isolated points.
We prove that every product variety
U
V
\mathcal{UV}
, where 𝒰 (respectively, 𝒱) is a non-abelian (respectively, a non-locally finite) variety, contains a condensed group.
In particular, there exist condensed groups of finite exponent.
As an application, we obtain some results on the structure of the isomorphism and elementary equivalence relations on the set of finitely generated groups in
U
V
\mathcal{UV}
.
Subject
Algebra and Number Theory
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1. Finitely presented condensed groups;Proceedings of the American Mathematical Society;2024-05-21