A generalized wreath product method for the enumeration of stereo and position isomers of polysubstituted organic compounds

1979 ◽  
Vol 51 (1) ◽  
pp. 37-54 ◽  
Author(s):  
K. Balasubramanian
Keyword(s):  
Organic Compounds ◽  
Wreath Product ◽  
Product Method ◽  
Generalized Wreath Product

Separable ultrametric spaces and their isometry groups

2014 ◽  
Vol 26 (6) ◽  
Author(s):  
Maciej Malicki
Keyword(s):  
Wreath Product ◽  
Isometry Group ◽  
Uniqueness Property ◽  
Isometry Groups ◽  
Ultrametric Spaces ◽  
Generalized Wreath Product ◽  
Group Construction

AbstractThe paper is devoted to a study of isometry groups of Polish ultrametric spaces. We explicitly describe isometry groups of spaces that are non-locally rigid and satisfy the property that distances between orbits under the action of the isometry group are realized by points. The type of group construction appearing here is a variant of the generalized wreath product. We prove that it has a natural universality and uniqueness property. As an application, we characterize Polish ultrametric spaces satisfying the above properties, whose isometry groups have uncountable strong cofinality.

scholarly journals Automorphism group of the variant of the lattice of partitions of a finite set

2020 ◽  
pp. 115-119
Author(s):  
O. G. Ganyushkin ◽  
O. O. Desiateryk
Keyword(s):  
Automorphism Group ◽  
Wreath Product ◽  
Direct Product ◽  
Automorphism Groups ◽  
Symmetric Groups ◽  
Natural Generalization ◽  
Generating Sets ◽  
Generalized Wreath Product ◽  
Finite Set

In this paper we consider variants of the lattice of partitions of a finite set and study automorphism groups of this variants. We obtain irreducible generating sets for of the lattice of partitions of a finite set. We prove that the automorphism group of the variant of the lattice of partitions of a finite set is a natural generalization of the wreath product. The first multiplier of this generalized wreath product is the direct product of the wreaths products, such that depends on the type of the variant generating partition and the second is defined by the certain set of symmetric groups.

scholarly journals CI-Property for Decomposable Schur Rings over an Abelian Group

2019 ◽  
Vol 26 (01) ◽  
pp. 147-160 ◽  
Author(s):  
István Kovács ◽  
Grigory Ryabov
Keyword(s):  
Finite Group ◽  
Abelian Group ◽  
Wreath Product ◽  
Direct Product ◽  
Elementary Abelian Group ◽  
Sufficient Condition ◽  
Schur Ring ◽  
Generalized Wreath Product ◽  
A Finite Group ◽  
Ci Property

A Schur ring over a finite group is said to be decomposable if it is the generalized wreath product of Schur rings over smaller groups. In this paper we establish a sufficient condition for a decomposable Schur ring over the direct product of elementary abelian groups to be a CI-Schur ring. By using this condition we offer short proofs for some known results on the CI-property for decomposable Schur rings over an elementary abelian group of rank at most 5.

The Tempo and mode(S) of Prebiotic Evolution

1997 ◽  
Vol 161 ◽  
pp. 419-429 ◽  
Author(s):  
Antonio Lazcano
Keyword(s):  
Origin Of Life ◽  
Organic Compounds ◽  
Biological Evolution ◽  
Current Evidence ◽  
Early Diversification ◽  
Time Period ◽  
The Galaxy ◽  
History Of ◽  
Widespread Phenomenon ◽  
The Origin Of Life

AbstractDifferent current ideas on the origin of life are critically examined. Comparison of the now fashionable FeS/H2S pyrite-based autotrophic theory of the origin of life with the heterotrophic viewpoint suggest that the later is still the most fertile explanation for the emergence of life. However, the theory of chemical evolution and heterotrophic origins of life requires major updating, which should include the abandonment of the idea that the appearance of life was a slow process involving billions of years. Stability of organic compounds and the genetics of bacteria suggest that the origin and early diversification of life took place in a time period of the order of 10 million years. Current evidence suggest that the abiotic synthesis of organic compounds may be a widespread phenomenon in the Galaxy and may have a deterministic nature. However, the history of the biosphere does not exhibits any obvious trend towards greater complexity or «higher» forms of life. Therefore, the role of contingency in biological evolution should not be understimated in the discussions of the possibilities of life in the Universe.

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