Several results on the action of graph automorphisms on ends and fibers are generalized for the case of metric ends. This includes results on the action of the automorphisms on the end space, directions of automorphisms, double rays which are invariant under a power of an automorphism and metrically almost transitive automorphism groups. It is proved that the bounded automorphisms of a metrical...

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...

Hyperplanes and hyperplane complements in the Segre product of partial linear spaces are investigated. The parallelism of such a complement is characterized in terms of the point-line incidence. Assumptions, under which the automorphisms of the complement are the restrictions of the automorphisms of the ambient space, are given. An affine covering for the Segre product of Veblenian gamma spaces...

A cellular automaton (CA) is a discrete dynamical system, and the transition graph is a representation of the CA’s phase space. Automorphisms of the transition graph correspond to symmetries of the phase space; studying how the total number of automorphisms varies with the number of cells on which the CA operates yields a (partial) classification of the space of CA rules according to their dyna...

We analyze the mapping class group Hx(W ) of automorphisms of the exterior boundary W of a compression body (Q,V ) of dimension 3 or 4 which extend over the compression body. Here V is the interior boundary of the compression body (Q,V ). Those automorphisms which extend as automorphisms of (Q,V ) rel V are called discrepant automorphisms, forming the mapping class group Hd(W ) of discrepant au...

In this paper is proved that the group of automorphisms of semi-group End(P [X]), if P is algebraically closed field, is generated by semi-inner automorphisms.

This paper studies several concepts about subgroups of automorphisms of linearly ordered relational structures. In particular, it focuses on conditions that are equivalent to the translations (automorphisms with no fixed points plus the identity) forming a homogeneous, Archimedean ordered group under the asymptotic order. For the automorphisms of an ordered relational structure, these propertie...

In this paper, we introduce the  probabilistic normed groups. Among other results, we investigate the continuityof inner automorphisms of a group and the continuity of left and right shifts in probabilistic group-norm. We also study midconvex functions defined  on probabilistic normed groups and  give  some results about locally boundedness of such  functions.

We give an algebro-geometric approach towards the dynamics of automorphisms/endomorphisms of projective varieties or compact Kähler manifolds, try to determine the building blocks of automorphisms /endomorphisms, and show the relation between the dynamics of automorphisms/endomorphisms and the geometry of the underlying manifolds.

For a substitution satisfying the Pisot, irreducible, unimodular condition, a tiling substitution plays a key role in the construction of Rauzy fractals (see [15, 3]). To try extending techniques developed for substitutions to automorphisms, [6] gives the way to construct Rauzy fractals by using tiling substitutions for automorphisms related to hyperbolic companion matrices of quadratic polynom...