Full paper in PDF:

$%W. S. Jassim, On the intersection of finitely generated subgroups of
free groups,
Rev. Mat. Univ. Complut. Madrid 9 (1996), no. 1, 67–84.%$

On the Intersection of Finitely Generated
Subgroups of Free Groups

W. S. JASSIM

P.O. Box 4286

Ádhamiyah (Bagdad) — Iraq

Ádhamiyah (Bagdad) — Iraq

Revised: April 25, 1995

ABSTRACT

Howson (1954) proved that the intersection of two finitely generated subgroups and of ranks and respectively is finitely generated. He proved that the rank of is at most . H. Neumann (1956, 1960) gave a better bound of . Burns (1971) further improved the general upper bound to (for ).

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 holds if or is of finite index in .

In this paper it is shown that the stronger bound always holds.

1991 Mathematics Subject Classification: 20E07.