Full paper in PDF:
$%W. S. Jassim, On the intersection of finitely generated subgroups of free groups, Rev. Mat. Univ. Complut. Madrid 9 (1996), no. 1, 6784.%$

On the Intersection of Finitely Generated Subgroups of Free Groups
P.O. Box 4286
Ádhamiyah (Bagdad) Iraq

Received: June 6, 1994
Revised: April 25, 1995

Howson (1954) proved that the intersection of two finitely generated subgroups H  and K  of ranks m  and n  respectively is finitely generated. He proved that the rank N  of H  /~\  K  is at most 2mn -m - n +1  . H. Neumann (1956, 1960) gave a better bound of 2mn -2n -2m + 3  . Burns (1971) further improved the general upper bound to N = 2mn - 3m - 2n + 4  (for m < n  ).

Imrich (1977) gave shorter proof of Neumann’s result and also Nickolas (1985) gave a simple proof for Burns’ result. Servatius (1983) gave a graphical proof for Burns’ result.

Burns (1969) showed that the stronger bound N = mn -n - m +2  holds if H  or K  is of finite index in F  .

In this paper it is shown that the stronger bound N = mn -n - m +2  always holds.

1991 Mathematics Subject Classification: 20E07.