Automorphisms of Partially Commutative Groups I: Linear Subgroups *

Automorphisms of Partially Commutative Groups II: Combinatorial Subgroups

Some combinatorial aspects of finite Hamiltonian groups

In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...

Groups Generated by Two Operators of the Same Prime Order Such That the Conjugates of One under the Powers of the Other Are Commutative. by Peopessok

IN a previous article,* devoted to a study of conjugate operators, attention was called to the fact that a complete set of conjugate operators which are not all relatively commutative is transformed under the group according to a substitution group which is at most triply transitive. It is easy to prove that this substitution group is at most doubly transitive, and, as the p conjugates of order...

Parabolic and Quasiparabolic Subgroups of Free Partially Commutative Groups

Let Γ be a finite graph and G be the corresponding free partially commutative group. In this paper we study subgroups generated by vertices of the graph Γ, which we call canonical parabolic subgroups. A natural extension of the definition leads to canonical quasiparabolic subgroups. It is shown that the centralisers of subsets of G are the conjugates of canonical quasiparabolic centralisers sat...

On Certain Questions of the Free Group Automorphisms Theory

Certain subgroups of the groups Aut(Fn) of automorphisms of a free group Fn are considered. Comparing Alexander polynomials of two poly-free groups Cb+4 and P4 we prove that these groups are not isomorphic, despite the fact that they have a lot of common properties. This answers the question of Cohen-Pakianathan-Vershinin-Wu from [8]. The questions of linearity of subgroups of Aut(Fn) are consi...