On outer automorphisms of Černikov -groups
On -groups with abelian automorphism group
On regular automorphisms of order 3 and Frobenius pairs.
On the Automorphism Group of a Finite Group Having No Non-Identity Normal Subgroup of Odd Order.
On the automorphism of a class of groups.
On the derived length of parasoluble groups
In this paper groups are considered inducing groups of power automorphisms on each factor of their derived series. In particular, it is proved that soluble groups with such property have derived length at most 3, and that this bound is best possible.
On the group of automorphisms of finite wreath products
On the isomorphism problem in the class of extensions of a free group by an infinite cyclic group.
On the lattice automorphisms of certain simple algebraic groups
-adic completions and automorphisms of nilpotent groups
Representations of (1,1)-knots
We present two different representations of (1,1)-knots and study some connections between them. The first representation is algebraic: every (1,1)-knot is represented by an element of the pure mapping class group of the twice punctured torus PMCG₂(T). Moreover, there is a surjective map from the kernel of the natural homomorphism Ω:PMCG₂(T) → MCG(T) ≅ SL(2,ℤ), which is a free group of rank two, to the class of all (1,1)-knots in a fixed lens space. The second representation is parametric: every...
Rings of Fricke Characters and Automorphism Groups of Free Groups.
Stabilization for the automorphisms of free groups with boundaries.
Stable actions of groups on real trees.
Stable rational cohomology of automorphism groups of free groups and the integral cohomology of moduli spaces of graphs.
It is not known whether or not the stable rational cohomology groups H*(Aut(F∞);Q) always vanish (see Hatcher in [5] and Hatcher and Vogtmann in [7] where they pose the question and show that it does vanish in the first 6 dimensions). We show that either the rational cohomology does not vanish in certain dimensions, or the integral cohomology of a moduli space of pointed graphs does not stabilize in certain other dimensions. Similar results are stated for groups of outer automorphisms. This yields...
Structure and Regidity in Hyperbolic Groups. I.
Sur les automorphismes extérieurs des groupes hyperboliques
Test elements and test rank of a free metabelian group.
The 4-string braid group has property RD and exponential mesoscopic rank
We prove that the braid group on 4 strings, its central quotient , and the automorphism group of the free group on 2 generators, have the property RD of Haagerup–Jolissaint. We also prove that the braid group is a group of intermediate mesoscopic rank (of dimension 3). More precisely, we show that the above three groups have exponential mesoscopic rank, i.e., that they contain exponentially many large flat balls which are not included in flats.
The abelianization of the Johnson kernel
We prove that the first complex homology of the Johnson subgroup of the Torelli group is a non-trivial, unipotent -module for all and give an explicit presentation of it as a -module when . We do this by proving that, for a finitely generated group satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that the first homology of its Johnson kernel is a nilpotent module over the corresponding Laurent polynomial ring, isomorphic to the...