Deficiency and commensurators
Deficiency and commensurators
Abstract We show that if π is the fundamental group of a 4-dimensional infrasolvmanifold then <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mo>-</m:mo> <m:mn>2</m:mn> </m:mrow> <m:mo>≤</m:mo> <m:mrow> <m:mi>def</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>π</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo>≤</m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> {-2\leq\mathrm{def}(\pi)\leq 0} , and give examples realizing each value allowed by our …