Metabelian groups: Full-rank presentations, randomness and Diophantine problems
Metabelian groups: Full-rank presentations, randomness and Diophantine problems
Abstract We study metabelian groups 𝐺 given by full rank finite presentations <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mo stretchy="false">⟨</m:mo> <m:mi>A</m:mi> <m:mo>∣</m:mo> <m:mi>R</m:mi> <m:mo stretchy="false">⟩</m:mo> </m:mrow> <m:mi mathvariant="script">M</m:mi> </m:msub> </m:math> \langle A\mid R\rangle_{\mathcal{M}} in the variety ℳ of metabelian groups. We prove that 𝐺 is a product of a free metabelian subgroup …