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 loop whose inner mappings are automorphisms is an automorphic loop (or A-loop). We characterize commutative (A-)loops with middle nucleus of index 2 and solve the isomorphism problem. Using this characterization and certain central extensions based on trilinear forms, we construct several classes of commutative A-loops of order a power of 2. We initiate the classification of commutative A-loo...

In this paper we study a key exchange protocol similar to the DiffieHellman key exchange protocol, using abelian subgroups of the automorphism group of a non-abelian nilpotent group. We also generalize group no. 92 of the Hall-Senior table [16] to an arbitrary prime p and show that, for those groups, the group of central automorphisms is commutative. We use these for the key exchange we are stu...

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...

The first absolute central moment is a statistical filter which measures the variability of the gray levels of the image with respect to the local mean. The analysis of the responses of the central and absolute central moments at noiseless isolated step discontinuities shows how the first absolute central moment can be usefully used to enhance these discontinuities. Moreover, experimental resul...

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.