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Monatshefte für Mathematik

, Volume 87, Issue 4, pp 273–280 | Cite as

On the number of subgroups of given index in the modular group

  • C. Godsil
  • W. Imrich
  • R. Razen
Article

Abstract

A new recurrence for the number of subgroups of given index in the modular group is derived. The proof requires the derivation of a recurrence for a sequenceanbn from recurrences for thean andbn. We show that this is always possible if thean andbn satisfy polynomial recurrences. We also include a short proof of a result ofW. W. Stothers on the parity of the number of subgroups of given index in the modular group.

Keywords

Short Proof Modular Group Polynomial Recurrence 
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References

  1. [1]
    Dey, I. M. S.: Schreier systems in free products. Proc. Glasgow Math. Assoc.7, 61–79 (1965).Google Scholar
  2. [2]
    Imrich, W.: On the number of subgroups of given index inSL 2 (Z). Archiv Math.31, 224–231 (1978).Google Scholar
  3. [3]
    Newman, M.: Asymptotic formulas related to free products of cyclic groups. Math. Comp.30, 838–846 (1976).Google Scholar
  4. [4]
    Stothers, W. W.: The number of subgroups of given index in the modular group. Proc. Royal Soc. Edinburgh78A, 105–112 (1977).Google Scholar
  5. [5]
    Stothers, W. W.: Free subgroups of the free product of cyclic groups. Math. Comp.32, 1274–1280 (1978).Google Scholar
  6. [6]
    Wohlfahrt, K.: Über einen Satz von Dey und die Modulgruppe. Archiv Math.29, 455–457 (1977).Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • C. Godsil
    • 1
  • W. Imrich
    • 2
  • R. Razen
    • 2
  1. 1.Department of MathematicsUniversity of MelbourneParkvilleAustralia
  2. 2.Institut für MathematikMontanuniversität LeobenLeobenAustria

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