Intersections of finitely generated free groups

On Intersections of Finitely Generated Subgroups of Free Groups

and asked if the factor 2 can be dropped. If one translates her approach (which is a slight modification of Howson's) to graph-theoretic terms, it easily shows that the answer is often "yes"in fact, for most U the answer is "yes" for all V. According to Gersten [G], the above problem has come to be known as the "Haana Neumann Conjecture." Using ideas of immersions of graphs originating from Sta...

Achievable Ranks of Intersections of Finitely Generated Free Groups

We answer a question due to A. Myasnikov by proving that all expected ranks occur as the ranks of intersections of finitely generated subgroups of free groups. Mathematics Subject Classification (2000): 20E05 Let F be a free group. Let H and K be nontrivial finitely generated subgroups of F . It is a theorem of Howson [1] that H ∩K has finite rank. H. Neumann proved in [2] that rank(H ∩K)− 1 ≤ ...

On finitely generated submonoids of free groups

We prove that the classes of graded monoids, regular monoids and Kleene monoids coincide for submonoids of free groups. We also prove that it is decidable whether or not a finitely generated submonoid of a free group is graded, and solve the homomorphism and isomorphism problems for graded submonoids of free groups. This generalizes earlier results for submonoids of free monoids. MSC: 20E05; 20...

Finitely Generated Abelian Groups

Finitely Generated Semiautomatic Groups

The present work shows that Cayley automatic groups are semiautomatic and exhibits some further constructions of semiautomatic groups and in particular shows that every finitely generated group of nilpotency class 3 is semiautomatic.