Intersections of automorphism fixed subgroups in the free group of rank three.
Intersections of Finitely Generated Subgroups of Free Groups and Resolutions de Graphs.
Inverse monoids and rational Schreier subsets of the free group.
Isomorphism classes and derived series of certain almost-free groups.
Large free subgroups of automorphism groups of ultrahomogeneous spaces
We consider the following notion of largeness for subgroups of . A group G is large if it contains a free subgroup on generators. We give a necessary condition for a countable structure A to have a large group Aut(A) of automorphisms. It turns out that any countable free subgroup of can be extended to a large free subgroup of , and, under Martin’s Axiom, any free subgroup of of cardinality less than can also be extended to a large free subgroup of . Finally, if Gₙ are countable groups, then...
Limit groups and groups acting freely on -trees.
Mapping tori of free group automorphisms are coherent.
Matrix theoretic interpretation of the classical Markoff theory. (L'interprétation matricielle de la théorie de Markoff classique.)
Maximal index automorphisms of free groups with no attracting fixed points on the boundary are Dehn twists.
Metabelian Representations and the Isomorphism Problem.
Moduli of graphs and automorphisms of free groups.
Monomorphisms of finitely generated free groups have finitely generated equalizers.
Morita classes in the homology of automorphism groups of free groups.
Nielsen reduction in free groups with operators
Non-free two-generator subgroups of SL2(Q).
The question of whether two parabolic elements A, B of SL2(C) are a free basis for the group they generate is considered. Some known results are generalized, using the parameter τ = tr(AB) - 2. If τ = a/b ∈ Q, |τ| < 4, and |a| ≤ 16, then the group is not free. If the subgroup generated by b in Z / aZ has a set of representatives, each of which divides one of b ± 1, then the subgroup of SL2(C) will not be free.
Numerical invariants of exponential groups and locally free approximation of the braid group.
On a Problem of Fox.
On an algorithm to decide whether a free group is a free factor of another
We revisit the problem of deciding whether a finitely generated subgroup is a free factor of a given free group . Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of and exponential in the rank of . We show that the latter dependency can be made exponential in the rank difference rank - rank, which often makes a significant change.
On an algorithm to decide whether a free group is a free factor of another
We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F. Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in the rank of F. We show that the latter dependency can be made exponential in the rank difference rank(F) - rank(H), which often makes a significant change.
On D. I. Moldavanskij's question on -separable subgroups of a free group.