1433-5883
Homogeneous number of free generators
Aka
Menny
Ecole Polytech Fed Lausanne, Sect Math, CH-1015 Lausanne, Switzerland
Gelander
Tsachik
Soifer
Gregory A.
2014
We address two questions of Simon Thomas. First, we show that for any n >= 3 one can find a four-generated free subgroup of SLn (Z) which is profinitely dense. More generally, we show that an arithmetic group Gamma that admits the congruence subgroup property has a profinitely-dense free subgroup with an explicit bound on its rank. Next, we show that the set of profinitely-dense, locally-free subgroups of such an arithmetic group Gamma is uncountable.
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