Condensed groups in product varieties
Condensed groups in product varieties
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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi mathvariant="script">U</m:mi> <m:mo></m:mo> <m:mi mathvariant="script">V</m:mi> </m:mrow> </m:math> \mathcal{UV} , where 𝒰 (respectively, 𝒱) is …