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math.GR2025
First-order sentences in random groups III
Olga Kharlampovich, Alexei Miasnikov, Rizos Sklinos
We show that a first-order sentence is almost surely true in a random group of density d<1/2 if and only if it is true in a non-abelian free group.
math.GR2025
The Diophantine problem in iterated wreath products of free abelian groups is undecidable
Olga Kharlampovich, Alexei Miasnikov
In this paper we prove that the Diophantine problem in iterated restricted wreath products of arbitrary non-trivial free abelian groups , of finite ranks…