s Prof. Paul Baginski Title: Definability and Nilpotence in Groups with Bounded Chains of Centralizers Abstract: A group G has bounded chains of centralizers (G is MC) if every chain of centralizers CG(A1) ≤ CG(A2) ≤ . . . is finite. While this class of groups is interesting in its own right, within the field of logic known as model theory, MC groups have been examined because they strictly con...

The Arnoux-Rauzy systems are defined in [5], both as symbolic on three letters and exchanges of six intervals the circle. In connection with a conjecture S.P. Novikov, we investigate dynamical properties interval exchanges, precise their relation systems, which was known only to be semi-conjugacy; order do this, define new system is an exchange nine (it described [3] for particular case). Our m...

‎Let $G$ be a finite group‎. ‎By $MT(G)=(m_1,cdots,m_k)$ we denote the type of‎ ‎conjugacy classes of maximal subgroups of $G$‎, ‎which implies that $G$ has exactly $k$ conjugacy classes of‎ ‎maximal subgroups and $m_1,ldots,m_k$ are the numbers of conjugates‎ ‎of maximal subgroups of $G$‎, ‎where $m_1leqcdotsleq m_k$‎. ‎In this paper‎, ‎we‎ ‎give some new characterizations of finite groups by ...

suppose $g$ is a finite group, $a$ and $b$ are conjugacy classes of $g$ and $eta(ab)$ denotes the number of conjugacy classes contained in $ab$. the set of all $eta(ab)$ such that $a, b$ run over conjugacy classes of $g$ is denoted by $eta(g)$.the aim of this paper is to compute $eta(g)$, $g in { d_{2n}, t_{4n}, u_{6n}, v_{8n}, sd_{8n}}$ or $g$ is a decomposable group of order $2pq$, a group of...

Fullerene chemistry is nowadays a well-established field of both theoretical and experimental investigations‎. This study considers the symmetry of small fullerenes cage C24 and C28‎. ‎Using PM3 program for C24 and C28 fullerenes, Oh and Td symmetry were confirmed, respectively‎. ‎ The mentioned algorithm to compute the automorphism group of these fullerenes with connectivity and geometry of th...

There have been several attempts to extend the notion of conjugacy from groups to monoids. The aim of this paper is study the decidability and independence of conjugacy problems for three of these notions (which we will denote by ∼p, ∼o, and ∼c) in certain classes of finitely presented monoids. We will show that in the class of polycyclic monoids, p-conjugacy is “almost” transitive, ∼c is stric...

PURPOSE Vertically skewed eye movements are induced by head tilt toward the shoulder (roll). Because vertical and torsional eye movements are tightly coupled both mechanically and neuronally, the purpose of the present study was to investigate the conjugacy of torsional eye movements during the Bielschowsky head tilt test (BHTT). Furthermore, the purpose was to investigate the influence of diff...

We construct two practical algorithms for twisted conjugacy classes of polycyclic groups. The first algorithm determines whether elements a group are conjugate given endomorphisms, under the condition that their Reidemeister coincidence number is finite. second representatives endomorphisms if finite, or returns “false” this infinite. also discuss theoretical extension these to polycyclic-by-fi...

The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We comp...

Given a short exact sequence of groups with certain conditions, 1 → F → G → H → 1, we prove that G has solvable conjugacy problem if and only if the corresponding action subgroup A Aut(F ) is orbit decidable. From this, we deduce that the conjugacy problem is solvable, among others, for all groups of the form Z2 Fm, F2 Fm, Fn Z, and Zn A Fm with virtually solvable action group A GLn(Z). Also, w...