Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4583588 | Journal of Algebra | 2017 | 5 Pages |
Abstract
Let nâ¥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 gâSL(n,Z) there exists hâSL(n,Z) such that [SL(n,Z):ãg,hmã]<â for every mâ¥1.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Chen Meiri,