Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Generators for all principal congruence subgroups of $ {\rm SL}(n,{\bf Z})$ with $ n\geq 3$


Authors: B. Sury and T. N. Venkataramana
Journal: Proc. Amer. Math. Soc. 122 (1994), 355-358
MSC: Primary 20H05
DOI: https://doi.org/10.1090/S0002-9939-1994-1239806-5
MathSciNet review: 1239806
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that there is a uniform bound for the numbers of generators for all principal congruence subgroups of $ {\text{SL}}(n,Z)$ for $ n \geq 3$. On the other hand, we show that the numbers are unbounded if we work with all arithmetic subgroups of $ {\text{SL}}(n,Z)$.


References [Enhancements On Off] (What's this?)

  • [B-M-S] H. Bass, J. Milnor, and J.-P. Serre, Solution of the congruence subgroup problem for $ {\text{SL}_{n}}\;(n \geq 3)$ and $ {\operatorname{Sp}_{2n}}\;(n \geq 2)$, Inst. Hautes Études Sci. Publ. Math. 33 (1967), 421-499. MR 0244257 (39:5574)
  • [K] M. Kneser, Strong approximation, Proc. Sympos. Pure Math., vol. 9, Amer. Math. Soc., Providence, RI, 1966, pp. 187-196. MR 0213361 (35:4225)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20H05

Retrieve articles in all journals with MSC: 20H05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1239806-5
Keywords: Congruence subgroup, finite generation
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society