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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
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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 𝑆𝐿_{𝑛}(𝑛≥3) and 𝑆𝑝_{2𝑛}(𝑛≥2), Inst. Hautes Études Sci. Publ. Math. 33 (1967), 59–137. MR 0244257
  • [K] Martin Kneser, Strong approximation, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 187–196. MR 0213361

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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

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