arXiv subjects
Publications and source records attributed to V. Metaftsis.
Let $G$ be a multiple HNN-extension of an infinite cyclic group. We will calculate the intersection $(N_{p}){_\omega}(G)$ of the normal subgroups of finite $p$-index in $G$ thus generalizing the result of Moldavanskii for Baumslag-Solitar groups. As a corollary we give necessary and sufficient conditions for $G$ to be residually finite $p$-group.
For a Generalized Baumslag-Solitar group $G$ with underling graph a tree, we calculate the intersection $\gamma_{\omega}(G)$ of the lower central series and the intersection $(N_{p})_{\omega}(G)$ of the subgroups of finite index some power of a prime $p$.
We investigate the Lie algebra of the Formanek-Procesi group FP(H) with base group H a right-angled Artin group. We show that the Lie algebra gr(FP(H)) has a presentation that is dictated by the group presentation. Moreover we show that FP(H) is a Magnus group.
For a Baumslag-Solitar group $G$ we calculate the intersection $γ_w(G)$ of all terms of the lower central sequence of $G$.Using this we are able to show that $[γ_w(G),G]=γ_w(G)$ thus answering a question of Bardakov and Neschadim. Finally we show that the quotient groups $γ_c(G)/γ_{c+1}(G)$ of the lower central series of $G$ are finite.
In the present work we investigate a subgroup $I_n$ of the McCool group $M_n$. We show that $I_n$ has solvable conjugacy problem. Next, we investigate its Lie Algebra gr($I_n$) and we find a presentation for it. Finally we show that gr($I_n$) is naturally embedded into the Andreadakis-Johnson Lie Algebra of the IA automorphisms of the free group $F_n$.
We prove that, for any positive integer $c$, the quotient group $γ_{c}(M_{3})/γ_{c+1}(M_{3})$ of the lower central series of the McCool group $M_{3}$ is isomorphic to two copies of the quotient group $γ_{c}(F_{3})/γ_{c+1}(F_{3})$ of the lower central series of a free group $F_{3}$ of rank $3$ as $\mathbb{Z}$-modules. Furthermore, we give a necessary and sufficient condition whether the associated graded Lie algebra ${\rm gr}(M_{3})$ of $M_3$ is naturally embedded into the Johnson Lie algebra ${\cal L}({\rm IA}(F_{3}))$ of the IA-automorphisms of $F_{3}$.
We prove that for any finitely generated relatively hyperbolic group G and any symmetric endomorphism f of G with relatively quasiconvex image, Fixf is relatively quasiconvex subgroup of G.
We prove that the Lie Algebra of the McCool group $M_3$ is torsion free. As a result we are able to give a presentation for the Lie Algebra of $M_3$. Furthermore, $M_3$ is a Magnus group.
We show that the K-FJCw holds for certain subgroups of Aut($F_n$) constructed from Hol($F_2$).
Quasitoric manifolds are manifolds that admit an action of the torus that is locally as the standard action of T^n on C^n. It is known that the quotients of such actions are nice manifolds with corners. We prove that such manifolds are equivariantly rigid i.e., that any other manifold that is T^n-homotopy equivalent to a quasitoric manifold, is T^n-homeomorphic to it.
We show that an HNN-extension with finitely generated abelian base group is Z-linear if and only if it is residually finite.
We show that the holomorph of the free group on two generators satisfies the Farrell-Jones Fibered Isomorphism Conjecture. As a consequence, we show that the lower K-theory of the above group vanishes.
We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable relatively hyperbolic group is residually finite. As a direct consequence, we obtain that the outer automorphism group of a limit group is residually finite.
We give necessary and sufficient conditions on the graph of a right-angled Artin group that determine whether the group is subgroup separable or not. Moreover, we investigate the profinite topology of the direct product of two free groups. We show that the profinite topology of the above group is strongly connected with the profinite topology of the free group of rank two.
Let F_n denote the free group generated by n letters. The purpose of this article is to show that Hol(F_2), the holomorph of the free group on two generators, is linear. Consequently, any split group extension of F_2 by a linear group H is linear. This result gives a large linear subgroup of Aut(F_3). A second application is that the mapping class group for genus one surfaces with two punctures is linear.
For a torsion free finitely generated nilpotent group G we naturally associate four finite dimensional nilpotent Lie algebras over a field of characteristic zero. We show that if G is a relatively free group of some variery of nilpotent groups then all the above Lie algebras are isomorphic. As a result, any two quasi-isometric relatively free nilpotent groups are isomorphic. Moreover let L be a relatively free nilpotent Lie algebra over Q generated by X. We give L the structure of a group by means of the Baker-Campbell-Hausdorff formula and we show that the subgroup H generated by X is relatively free in some variety of nilpotent groups, is Magnus and certain Lie algebras associated to H are isomorphic. This isomorphism is extended to relatively free residually torsion-free nilpotent groups. Finally, we give an example that demonstrates that this is not always the case with finitely generated Magnus nilpotent groups.
We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable hyperbolic group is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely generated Fuchsian group and of every free-by-finite group is resudually finite. We also generalize the main result for relatively hyperbolic groups.