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.