Inventiones mathematicae

, Volume 108, Issue 1, pp 29-36

First online:

On the intersection of subgroups of a free group

  • Gábor TardosAffiliated withDIMACS Center, Rutgers UniversityMathematical Research Institute, Hungarian Academy of Sciences

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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′).