The Steinberg Function of a Finite Lie Algebra.
The structure of a complete -group
The structure of disjoint iteration groups on the circle
The aim of the paper is to investigate the structure of disjoint iteration groups on the unit circle , that is, families of homeomorphisms such that and each either is the identity mapping or has no fixed point ( is an arbitrary -divisible nontrivial (i.e., ) abelian group).
The structure of finite p-groups: effective proof of the coclass conjectures.
The structure of -free nilpotent groups of step 3.
The structure of the rings assigned to group varieties
The subgroups of , or how to compute the table of marks of a finite group.
The surjectivity problem for one-generator, one-relator extensions of torsion-free groups.
The Symmetries of Classes of Elements in a Free Group of Rank Two.
The symmetry of intersection numbers in group theory.
The tame automorphism group of an affine quadric threefold acting on a square complex
We study the group of tame automorphisms of a smooth affine -dimensional quadric, which we can view as the underlying variety of . We construct a square complex on which the group admits a natural cocompact action, and we prove that the complex is and hyperbolic. We propose two applications of this construction: We show that any finite subgroup in is linearizable, and that satisfies the Tits alternative.
The Tits alternative for . I: Dynamics of exponentially-growing automorphisms.
The Topological Version of Groups Generated by Reflections.
The topology of the relative character varieties of a quadruply-punctured sphere.
The triangle groups
The unit group of .
The upper central series of some matrix groups
The virtual and universal braids
We study the structure of the virtual braid group. It is shown that the virtual braid group is a semi-direct product of the virtual pure braid group and the symmetric group. Also, it is shown that the virtual pure braid group is a semi-direct product of free groups. From these results we obtain a normal form of words in the virtual braid group. We introduce the concept of a universal braid group. This group contains the classical braid group and has as quotients the singular braid group, virtual...
The virtual cohomological dimension of the mapping class group of an orientable surface.
The virtual Haken conjecture: Experiments and examples.