COSET: a program for deriving and testing merohedral and pseudo-merohedral twin laws

2014 ◽  
Vol 47 (1) ◽  
pp. 467-470 ◽  
Author(s):  
Paul D. Boyle
Keyword(s):  
Left Coset

COSETis a program written in ISO C99 with POSIX extensions which uses left coset decompositions to determine possible merohedral and pseudo-merohedral twin laws. In addition to a stand-alone program, the code may be compiled as a Python extension module. The program can createSHELXLinstruction files which incorporate the appropriate TWIN and BASF instructions for the possible twin law(s).COSETmay also be directed to execute a locally installed copy of theSHELXLbinary executable to test the candidate twin laws in trial refinements. This facilitates the quick screening and assessment of possible twin laws.

A Classification of Homogeneous Surfaces

1981 ◽  
Vol 33 (5) ◽  
pp. 1097-1110 ◽  
Author(s):  
A. T. Huckleberry ◽  
E. L. Livorni
Keyword(s):  
Automorphism Group ◽  
Homogeneous Space ◽  
Lie Group ◽  
Compact Complex Manifold ◽  
Coset Space ◽  
Left Coset ◽  
Detailed Classification ◽  
Dimensional Ball ◽  
Lie Subgroup

Throughout this paper a surface is a 2-dimensional (not necessarily compact) complex manifold. A surface X is homogeneous if a complex Lie group G of holomorphic transformations acts holomorphically and transitively on it. Concisely, X is homogeneous if it can be identified with the left coset space G/H, where if is a closed complex Lie subgroup of G. We emphasize that the assumption that G is a complex Lie group is an essential part of the definition. For example, the 2-dimensional ball B2 is certainly “homogeneous” in the sense that its automorphism group acts transitively. But it is impossible to realize B2 as a homogeneous space in the above sense. The purpose of this paper is to give a detailed classification of the homogeneous surfaces. We give explicit descriptions of all possibilities.

Left coset extensions

1974 ◽  
Vol 7 (1-4) ◽  
pp. 200-263 ◽  
Author(s):  
Pierre Antoine Grillet
Keyword(s):  
Left Coset

Left Coset Invariance and Relativistic Invariance

1999 ◽  
Vol 27 (2) ◽  
pp. 57-72 ◽  
Author(s):  
W. N. Polyzou
Keyword(s):  
Relativistic Invariance ◽  
Left Coset

scholarly journals Character amenability and contractibility of some Banach algebras on left coset spaces

2016 ◽  
Vol 7 (4) ◽  
pp. 564-572
Author(s):  
M. Ramezanpour ◽  
N. Tavallaei ◽  
B. Olfatian Gillan
Keyword(s):  
Banach Algebras ◽  
Left Coset ◽  
Character Amenability ◽  
Coset Spaces

scholarly journals On Weak Graded Rings II

2019 ◽  
Vol 12 (2) ◽  
pp. 332-347
Author(s):  
Najla SH. Al-Subaie ◽  
Mohammed Mosa Al-shomrani
Keyword(s):  
Finite Group ◽  
Graded Rings ◽  
Left Coset ◽  
Left Action ◽  
A Finite Group

The G-weak graded rings are rings graded by a set G of left coset representatives for the left action of a subgroup H of a finite group X. The main aim of this article is to study the concept of G-weak graded rings and continue the investigation of their properties. Moreover, some results concerning G-weak graded rings of fractions are derived. Finally, some additional examples of G-weak graded rings are provided.

Abstract measure algebras over homogeneous spaces of compact groups

2018 ◽  
Vol 29 (01) ◽  
pp. 1850005 ◽  
Author(s):  
Arash Ghaani Farashahi
Keyword(s):  
Compact Group ◽  
Systematic Study ◽  
Measure Space ◽  
Closed Subgroup ◽  
Homogeneous Spaces ◽  
Compact Groups ◽  
Coset Space ◽  
Left Coset ◽  
Abstract Measure

This paper presents a systematic study for abstract Banach measure algebras over homogeneous spaces of compact groups. Let [Formula: see text] be a closed subgroup of a compact group [Formula: see text] and [Formula: see text] be the left coset space associated to the subgroup [Formula: see text] in [Formula: see text]. Also, let [Formula: see text] be the Banach measure space consists of all complex measures over [Formula: see text]. Then we introduce the abstract notions of convolution and involution over the Banach measure space [Formula: see text].

On a Theorem of Cohen and Lyndon About Free Bases for Normal Subgroups

1972 ◽  
Vol 24 (6) ◽  
pp. 1086-1091 ◽  
Author(s):  
A. Karrass ◽  
D. Solitar
Keyword(s):  
Normal Subgroup ◽  
Free Product ◽  
Double Coset ◽  
Normal Subgroups ◽  
Left Coset ◽  
Coset Representative ◽  
Representative System

Let S(≠1) be a subgroup of a group G. We consider the question: when are the conjugates of S “as independent as possible“? Specifically, suppose SG (the normal subgroup generated by S in G) is the free product II*S0α where and gα ranges over a subset J of G. Then J must be part of a (left) coset representative system for G mod SG. N where N is the normalizer of S in G. (For, g ∊ SGgαN implies Sg is conjugate to Sgα in SG; however, distinct non-trivial free factors of a free product are never conjugate.)We say that SG is the free product of maximally many conjugates of S in G if SG = II*Sgα where gα ranges over a (complete) left coset representative system for G mod SGN (or equivalently, gα ranges over a double coset representative system for G mod (SG, N)); in this case we say briefly that S has the fpmmc property in G.

ABSTRACT HARMONIC ANALYSIS OF RELATIVE CONVOLUTIONS OVER CANONICAL HOMOGENEOUS SPACES OF SEMIDIRECT PRODUCT GROUPS

2016 ◽  
Vol 101 (2) ◽  
pp. 171-187 ◽  
Author(s):  
ARASH GHAANI FARASHAHI
Keyword(s):  
Harmonic Analysis ◽  
Homogeneous Space ◽  
Semidirect Product ◽  
Homogeneous Spaces ◽  
Continuous Homomorphism ◽  
Compact Groups ◽  
Coset Space ◽  
Unified Approach ◽  
Left Coset ◽  
Semidirect Product Groups

This paper presents a structured study for abstract harmonic analysis of relative convolutions over canonical homogeneous spaces of semidirect product groups. Let $H,K$ be locally compact groups and $\unicode[STIX]{x1D703}:H\rightarrow \text{Aut}(K)$ be a continuous homomorphism. Let $G_{\unicode[STIX]{x1D703}}=H\ltimes _{\unicode[STIX]{x1D703}}K$ be the semidirect product of $H$ and $K$ with respect to $\unicode[STIX]{x1D703}$ and $G_{\unicode[STIX]{x1D703}}/H$ be the canonical homogeneous space (left coset space) of $G_{\unicode[STIX]{x1D703}}/H$. We present a unified approach to the harmonic analysis of relative convolutions over the canonical homogeneous space $G_{\unicode[STIX]{x1D703}}/H$.

scholarly journals Fuzzy cosets in AG-groups

2021 ◽  
Vol 7 (3) ◽  
pp. 3321-3344
Author(s):  
Aman Ullah ◽  
◽  
Muhammad Ibrahim ◽  
Tareq Saeed ◽  
◽  
...  
Keyword(s):  
Group Theory ◽  
Index Number ◽  
Left Coset ◽  
Lagrange's Theorem

<abstract><p>In this paper, the notion of fuzzy AG-subgroups is further extended to introduce fuzzy cosets in AG-groups. It is worth mentioning that if $ A $ is any fuzzy AG-subgroup of $ G $, then $ \mu_{A}(xy) = \mu_{A}(yx) $ for all $ x, \, y\in G $, i.e. in AG-groups each fuzzy left coset is a fuzzy right coset and vice versa. Also, fuzzy coset in AG-groups could be empty contrary to fuzzy coset in group theory. However, the order of the nonempty fuzzy coset is the same as the index number $ [G:A] $. Moreover, the notions of fuzzy quotient AG-subgroup, fuzzy AG-subgroup of the quotient (factor) AG-subgroup, fuzzy homomorphism of AG-group and fuzzy Lagrange's theorem of finite AG-group is also introduced.</p></abstract>

Sign in / Sign up

Export Citation Format

Share Document