Papers and preprints of Inna
Bumagin(a).
The isomorphism problem
for finitely generated fully residually free groups (joint
with O. Kharlampovich and A. Miasnikov), submitted.
Abstract.
We prove that the isomorphism problem for finitely generated fully residually
free groups (or F
-groups for short) is decidable. We also show that each freely
indecomposable F
-group G has a decomposition that is invariant under automorphisms of G,
and obtain a structure theorem for the group of outer automorphisms Out(G).
On definitions of relatively
hyperbolic groups, Contemporary Mathematics series, volume
372(2005) "Geometric methods in Group Theory",
J.Burillo,
S.Cleary, M.Elder, J.Taback and E.Ventura, editors.
Abstract. The purpose of this note is to provide a short alternate proof which (combined with a result of Szczepanski) shows that a group that
is relatively hyperbolic in the sense of the definition of Gromov is relatively hyperbolic in the sense of the definition of Farb.
Every group is an outer automorphism
group of a finitely generated group, (joint with D. Wise),
Journal of Pure and Applied Algebra, 200(2005), 137-147.
Abstract. We show that every countable group Q is isomorphic to Out(N) where N is a finitely generated subgroup of a countable
C'(1/6) small-cancellation group G. Furthermore, when Q is finitely presented, we can choose G to be finitely presented and residually finite.
The conjugacy problem for relatively hyperbolic groups, Algebraic and Geometric Topology, 4(2004), 1013-1040.
Abstract. Solvability of the conjugacy problem for relatively hyperbolic groups was announced by M. Gromov. Using the definition
of B. Farb of a relatively hyperbolic group, we prove this assertion and conclude that the conjugacy problem is solvable for
fundamental groups of complete, finite-volume, negatively curved manifolds, and for finitely generated fully residually free groups.
Subgroups of torsion-free hyperbolic groups have the Hopf property , Geometriae Dedicata, 106(1), 2004, 211-230.
Abstract. A group is said to have the Hopf property if every surjective endomorphism of the group is injective. We show that
finitely generated subgroups of torsion-free hyperbolic groups are Hopf. Our proof generalizes a theorem of Z Sela.
k-generated groups with (k-1)-generated subgroups all free , International Journal of Algebra and Comp., Vol.11, No.5 (2001) 507--524.
Effective conditions that ensure the above property for a group, are proved by methods of combinatorial group theory. Important ingredients of the proof are
Greendlinger's Lemma and Stallings' construction of the folded finite graph with a given fundamental group.
Examples of amalgamated products of groups
,
Abstract. The rank of a group G is the minimal number of elements that
generate G.
For any natural number n we construct two groups, G of rank r(G)=n and H of rank r(H)=2n
such that their amalgamated product over an infinite cyclic
subgroup, malnormal in both factors, is generated by 2n=r(G)+r(H)-n elements. We also
consider an example of the free product G of n factors amalgamated over a subgroup A such that the
rank of G equals n+1
and the rank of A is greater or
equal 1.
This example realizes the lower bound given in an inequality proven by R.
Weidmann.