Inventiones mathematicae

, Volume 108, Issue 1, pp 29–36

On the intersection of subgroups of a free group

  • Gábor Tardos
Article

Summary

The Hanna Neumann Conjecture says that the intersection of subgroups of rankn+1 andm+1 of a free group has rank at mostnm+1. This paper proves the conjecture for the casem=1. (See Theorem 1.) Our methods imply that the strengthened Hanna Neumann Conjecture is also true in this case (Theorem 2′).

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References

  1. 1.
    Burns, R.G.: On the intersection of finitely generated subgroups of a free group. Math. Z.119, 121–130 (1971)Google Scholar
  2. 2.
    Burns, R.G., Imrich, W., Servatius, B.: Remarks on the intersection of finitely generated subgroups of a free group. Can. Math. Bull.29, 204–207 (1986)Google Scholar
  3. 3.
    Gersten, S.M.: Intersections of finitely generated subgroups of free groups and resolutions of graphs. Invent. Math.71, 567–591 (1983)Google Scholar
  4. 4.
    Howson, A.G.: On the intersection of finitely generated free groups. J Lond. Math. Soc.29, 428–434 (1954)Google Scholar
  5. 5.
    Imrich, W.: Subgroup theorems and graphs. In: Little, C.H.C. (ed.) Combinatorial Mathematics V. (Lect. Notes Math., vol. 622, pp. 1–27) Berlin Heidelberg New York: Springer 1977Google Scholar
  6. 6.
    Neumann, H.: On the intersection of finitely generated free groups. Publ. Math.4, 186–189, (1956); Addendum Publ. Math.5, 128 (1957/58)Google Scholar
  7. 7.
    Neumann, W.D.: On intersections of finitely generated subgroups of free groups. In: Groups-Canberra 1989. (Lect. Notes Math., vol. 1456, pp. 161–170) Berlin Heidelberg New York: Springer 1990Google Scholar
  8. 8.
    Nickolas, P.: Intersections of finitely generated free groups. Bull. Aust. Math. Soc.31, 339–348 (1985)Google Scholar
  9. 9.
    Servatius, B.: A short proof of a theorem of Burns. Math. Z.184, 133–137 (1983)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Gábor Tardos
    • 1
    • 2
  1. 1.DIMACS CenterRutgers UniversityPiscatawayUSA
  2. 2.Mathematical Research InstituteHungarian Academy of SciencesHungary

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