A family of flat Minkowski planes admitting 3-dimensional simple groups of automorphisms

2004 ◽  
Vol 4 (3) ◽  
Author(s):  
Günter F. Steinke
Keyword(s):  
Simple Groups ◽  
Minkowski Planes ◽  
3 Dimensional ◽  
Groups Of Automorphisms

scholarly journals Simple groups of automorphisms of trees determined by their actions on finite subtrees

2015 ◽  
Vol 18 (2) ◽  
Author(s):  
Christopher Banks ◽  
Murray Elder ◽  
George A. Willis
Keyword(s):  
Simple Groups ◽  
Automorphisms Of Trees ◽  
Groups Of Automorphisms

AbstractWe introduce the notion of the

scholarly journals Three-dimensional connected groups of automorphisms of toroidal circle planes

2020 ◽  
Vol 20 (4) ◽  
pp. 585-594
Author(s):  
Brendan Creutz ◽  
Duy Ho ◽  
Günter F. Steinke
Keyword(s):  
Lie Group ◽  
Three Dimensional ◽  
Minkowski Planes ◽  
Point Set ◽  
Groups Of Automorphisms ◽  
Full Classification

AbstractWe contribute to the classification of toroidal circle planes and flat Minkowski planes possessing three-dimensional connected groups of automorphisms. When such a group is an almost simple Lie group, we show that it is isomorphic to PSL(2, ℝ). Using this result, we describe a framework for the full classification based on the action of the group on the point set.

scholarly journals DEFINABLY SIMPLE STABLE GROUPS WITH FINITARY GROUPS OF AUTOMORPHISMS

2019 ◽  
Vol 84 (02) ◽  
pp. 704-712
Author(s):  
ULLA KARHUMÄKI
Keyword(s):  
Finite Fields ◽  
Finite Groups ◽  
Simple Groups ◽  
Stable Group ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Groups Of Automorphisms ◽  
Groups Of Lie Type

AbstractWe prove that infinite definably simple locally finite groups of finite centraliser dimension are simple groups of Lie type over locally finite fields. Then, we identify conditions on automorphisms of a stable group that make it resemble the Frobenius maps, and allow us to classify definably simple stable groups in the specific case when they admit such automorphisms.

Three-Dimensional Reconstruction Using Stereo Pairs from Serial Thick Sections

1977 ◽  
Vol 35 ◽  
pp. 562-563
Author(s):  
Robert Glaeser ◽  
Thomas Bauer ◽  
David Grano
Keyword(s):  
Three Dimensional ◽  
Dimensional Structure ◽  
Serial Sections ◽  
Thin Sections ◽  
3 Dimensional ◽  
Transmission Electron ◽  
Freeze Dried ◽  
Dimensional Reconstruction ◽  
Stereo Imagery ◽  
Whole Mounts

In transmission electron microscopy, the 3-dimensional structure of an object is usually obtained in one of two ways. For objects which can be included in one specimen, as for example with elements included in freeze- dried whole mounts and examined with a high voltage microscope, stereo pairs can be obtained which exhibit the 3-D structure of the element. For objects which can not be included in one specimen, the 3-D shape is obtained by reconstruction from serial sections. However, without stereo imagery, only detail which remains constant within the thickness of the section can be used in the reconstruction; consequently, the choice is between a low resolution reconstruction using a few thick sections and a better resolution reconstruction using many thin sections, generally a tedious chore. This paper describes an approach to 3-D reconstruction which uses stereo images of serial thick sections to reconstruct an object including detail which changes within the depth of an individual thick section.

Structural preservation and absolute contrast of catalase crystal sections prepared with tannic acid

1983 ◽  
Vol 41 ◽  
pp. 448-449
Author(s):  
C.W. Akey ◽  
M. Szalay ◽  
S.J. Edelstein
Keyword(s):  
Tannic Acid ◽  
Beef Heart ◽  
X Rays ◽  
Screw Axis ◽  
General Applicability ◽  
Thin Sections ◽  
Beef Liver ◽  
3 Dimensional ◽  
Dimensional Reconstruction ◽  
Structural Preservation

Three methods of obtaining 20 Å resolution in sectioned protein crystals have recently been described. They include tannic acid fixation, low temperature embedding and grid sectioning. To be useful for 3-dimensional reconstruction thin sections must possess suitable resolution, structural fidelity and a known contrast. Tannic acid fixation appears to satisfy the above criteria based on studies of crystals of Pseudomonas cytochrome oxidase, orthorhombic beef liver catalase and beef heart F1-ATPase. In order to develop methods with general applicability, we have concentrated our efforts on a trigonal modification of catalase which routinely demonstrated a resolution of 40 Å. The catalase system is particularly useful since a comparison with the structure recently solved with x-rays will permit evaluation of the accuracy of 3-D reconstructions of sectioned crystals.Initially, we re-evaluated the packing of trigonal catalase crystals studied by Longley. Images of the (001) plane are of particular interest since they give a projection down the 31-screw axis in space group P3121. Images obtained by the method of Longley or by tannic acid fixation are negatively contrasted since control experiments with orthorhombic catalase plates yield negatively stained specimens with conditions used for the larger trigonal crystals.

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