Article ID Journal Published Year Pages File Type
4583588 Journal of Algebra 2017 5 Pages PDF
Abstract
Let n≥3. Lubotzky [2] asked if every finite index subgroup of SL(n,Z) contains a finite index subgroup which is generated by two elements. Venkataramana [11] proved that every finite index subgroup of SL(n,Z) contains a finite index subgroup which is generated by three elements. Since then it was widely believed that the answer to Lubotzky's question is positive and we show that this is indeed the case. In fact, we prove a stronger statement: for “almost every” element g∈SL(n,Z) there exists h∈SL(n,Z) such that [SL(n,Z):〈g,hm〉]<∞ for every m≥1.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
,