Generators for all principal congruence subgroups of $\textrm {SL}(n,\textbf {Z})$ with $n\geq 3$
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- by B. Sury and T. N. Venkataramana PDF
- Proc. Amer. Math. Soc. 122 (1994), 355-358 Request permission
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
- H. Bass, J. Milnor, and J.-P. Serre, Solution of the congruence subgroup problem for $\textrm {SL}_{n}\,(n\geq 3)$ and $\textrm {Sp}_{2n}\,(n\geq 2)$, Inst. Hautes Γtudes Sci. Publ. Math. 33 (1967), 59β137. MR 244257
- Martin Kneser, Strong approximation, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp.Β 187β196. MR 0213361
Additional Information
- © Copyright 1994 American Mathematical Society
- 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