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