TY - EJOUR
DO - 10.1515/jgt-2014-0001
AB - 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.
T1 - Homogeneous number of free generators
IS - 4
DA - 2014
AU - Aka, Menny
AU - Gelander, Tsachik
AU - Soifer, Gregory A.
JF - Journal Of Group Theory
SP - 525-539
VL - 17
EP - 525-539
PB - Walter De Gruyter Gmbh
PP - Berlin
ID - 201252
SN - 1433-5883
ER -