On the multiplier of a group with nontrivial center

1995 ◽  
Vol 47 (4) ◽  
pp. 634-639
Author(s):  
�. M. Zhmud'
Keyword(s):  
Nontrivial Center

scholarly journals Separating conjugates in amalgamated free products and HNN extensions

1980 ◽  
Vol 29 (1) ◽  
pp. 35-51 ◽  
Author(s):  
Joan L. Dyer
Keyword(s):  
Nilpotent Groups ◽  
Conjugacy Classes ◽  
Free Products ◽  
Amalgamated Free Products ◽  
Hnn Extensions ◽  
Nontrivial Center ◽  
One Relator Groups ◽  
Amalgamated Subgroup ◽  
Conjugacy Separable ◽  
Base Group

AbstractA group G is termed conjugacy separable (c.s.) if any pair of distinct conjugacy classes may be mapped to distinct conjugacy classes in some finite epimorph of G. The free product of A and B with cyclic amalgamated subgroup H is shown to be c.s. if A and B are both free, or are both finitely generated nilpotent groups. Further, one-relator groups with nontrivial center and HNN extensions with c.s. base group and finite associated subgroups are also c.s.

scholarly journals On a 2-knot group with nontrivial center

1982 ◽  
Vol 25 (3) ◽  
pp. 321-326 ◽  
Author(s):  
Katsuyuki Yoshikawa
Keyword(s):  
Nontrivial Center ◽  
Trivial Center

Jonathan A. Hillman asked “Must a 2-knot whose group has non-trivial center be fibered?” We will answer this question negatively.

scholarly journals Superselection Structures for C*-Algebras with Nontrivial Center

1997 ◽  
Vol 09 (07) ◽  
pp. 785-819 ◽  
Author(s):  
Hellmut Baumgärtel ◽  
Fernando Lledó
Keyword(s):  
Fixed Point ◽  
Compact Group ◽  
C Algebras ◽  
Nontrivial Center ◽  
Relative Commutant ◽  
Fixed Point Algebra

We present and prove some results within the framework of Hilbert C*-systems [Formula: see text] with a compact group [Formula: see text]. We assume that the fixed point algebra [Formula: see text] of [Formula: see text] has a nontrivial center [Formula: see text] and its relative commutant w.r.t. ℱ coincides with [Formula: see text], i.e. we have [Formula: see text]. In this context we propose a generalization of the notion of an irreducible endomorphism and study the behaviour of such irreducibles w.r.t. [Formula: see text]. Finally, we give several characterizations of the stabilizer of [Formula: see text].

Groups of finite Morley rank with transitive group automorphisms

1989 ◽  
Vol 54 (3) ◽  
pp. 1080-1082
Author(s):  
Ali Nesin
Keyword(s):  
Finite Order ◽  
Short Note ◽  
Algebraic Groups ◽  
Transitive Group ◽  
Simple Groups ◽  
Morley Rank ◽  
Nontrivial Center ◽  
Finite Morley Rank ◽  
Group Automorphisms

The aim of this short note is to prove the following result:Theorem. Let G be a group of finite Morley rank with Aut G acting transitively on G/{1}. Then G is either abelian or a bad group.Bad groups were first defined by Cherlin [Ch]: these are groups of finite Morley rank without solvable and nonnilpotent connected subgroups. They have been investigated by the author [Ne 1], Borovik [Bo], Corredor [Co], and Poizat and Borovik [Bo-Po]. They are not supposed to exist, but we are far from proving their nonexistence. This is one of the major obstacles to proving Cherlin's conjecture: infinite simple groups of finite Morley rank are algebraic groups.If the group G of the theorem is finite, then it is well known that G ≈ ⊕Zp for some prime p: clearly all elements of G have the same order, say p, a prime. Thus G is a finite p-group, so has a nontrivial center. But Aut G acts transitively; thus G is abelian. Since it has exponent p, G ≈ ⊕Zp.The same proof for infinite G does not work even if it has finite Morley rank, for the following reasons:1) G may not contain an element of finite order.2) Even if G does contain an element of finite order, i.e. if G has exponent p, we do not know if G must have a nontrivial center.

scholarly journals On the power-commutative kernel of locally nilpotent groups

2005 ◽  
Vol 2005 (17) ◽  
pp. 2719-2722
Author(s):  
Costantino Delizia ◽  
Chiara Nicotera
Keyword(s):  
Finite Groups ◽  
Nilpotent Groups ◽  
Nontrivial Center ◽  
Locally Nilpotent Groups ◽  
Locally Nilpotent

We define the power-commutative kernel of a group. In particular, we describe the power-commutative kernel of locally nilpotent groups, and of finite groups having a nontrivial center.

Cohomology of Lie algebras with a nontrivial center

1984 ◽  
Vol 25 (3) ◽  
pp. 443-444 ◽  
Author(s):  
Bani Mitra ◽  
B. R. Sitaram ◽  
K. C. Tripathy
Keyword(s):  
Lie Algebras ◽  
Nontrivial Center ◽  
Cohomology Of Lie Algebras

Subalgebras of the algebra of a conformal group with nontrivial center

1990 ◽  
Vol 33 (5) ◽  
pp. 416-419
Author(s):  
V. G. Bagrov ◽  
B. F. Samsonov ◽  
A. V. Shapovalov ◽  
I. V. Shirokov
Keyword(s):  
Conformal Group ◽  
Nontrivial Center

scholarly journals Improving Center Vortex Detection by Usage of Center Regions as Guidance for the Direct Maximal Center Gauge

Particles ◽  
2019 ◽  
Vol 2 (4) ◽  
pp. 491-498 ◽  
Author(s):  
Rudolf Golubich ◽  
Manfried Faber
Keyword(s):  
Simulated Annealing ◽  
Magnetic Flux ◽  
Degrees Of Freedom ◽  
Chiral Symmetry Breaking ◽  
String Tension ◽  
Local Maxima ◽  
Vortex Model ◽  
Center Vortex ◽  
Nontrivial Center ◽  
Vortex Detection

The center vortex model of quantum chromodynamic states that vortices, a closed color-magnetic flux, percolate the vacuum. Vortices are seen as the relevant excitations of the vacuum, causing confinement and dynamical chiral symmetry breaking. In an appropriate gauge, as direct maximal center gauge, vortices are detected by projecting onto the center degrees of freedom. Such gauges suffer from Gribov copy problems: different local maxima of the corresponding gauge functional can result in different predictions of the string tension. By using nontrivial center regions—that is, regions whose boundary evaluates to a nontrivial center element—a resolution of this issue seems possible. We use such nontrivial center regions to guide simulated annealing procedures, preventing an underestimation of the string tension in order to resolve the Gribov copy problem.

Method of Rotation of Geometrical Objects Around the Curvilinear Axis

2017 ◽  
Vol 5 (3) ◽  
pp. 45-50 ◽  
Author(s):  
И. Беглов ◽  
I. Beglov ◽  
Вячеслав Рустамян ◽  
Vyacheslav Rustamyan
Keyword(s):  
Rotation Axis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Straight Line Segment ◽  
Finite Radius ◽  
Straight Line ◽  
Nontrivial Center ◽  
Dupin Cyclides ◽  
Geometric Techniques

Rotation is the motion of geometric objects along a circle. This is one of geometric techniques used to form lines and surfaces. In this paper has been considered the rotation of objects in a three-dimensional space around a straight axis. It is known that a straight line can be considered as a particular case of a circle with a radius equal to infinity. Such circle’s center is at infinite distance from the considered straight line segment. Then in the general case, the rotation axis is a closed curve, for example, a circle with a radius of finite magnitude. Rotation of a point around a straight axis now splits into two trajectories. One of them is a circle with a radius, the second is a straight line crossing with the axis, and the center of this trajectory is at an infinite distance from the point. The method of point rotation about an axis of finite radius was considered. Note that a circle is a special case of an ellipse. When the actual focus of the circle is stratified into two, the line itself loses its curvature constancy, and is called an ellipse. The point, rotating around the elliptical axis, is stratified into four ones, forming four circles (trajectories). Axis foci appearing in turn in the role of the main one determine two trajectories by each with a trivial and nontrivial center of rotation. We have considered the variant for arrangement of the generating circle so that its center coincided with one of the elliptic axis’s foci. The obtained surfaces are a pair of co-axial Dupin cyclides, since they have identical properties. Changing the circle generatrix radius, other things being equal, we get different types of closed cyclides.

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