The Double Chain Condition in Cyclic Operator Groups

1947 ◽  
Vol 69 (1) ◽  
pp. 37 ◽  
Author(s):  
Reinhold Baer
Keyword(s):  
Chain Condition ◽  
Double Chain ◽  
Cyclic Operator

GROUPS SATISFYING THE DOUBLE CHAIN CONDITION ON ABELIAN SUBGROUPS

2018 ◽  
Vol 99 (2) ◽  
pp. 212-218 ◽  
Author(s):  
MATTIA BRESCIA ◽  
ALESSIO RUSSO
Keyword(s):  
Chain Condition ◽  
Double Sequences ◽  
Property A ◽  
Double Chain ◽  
Abelian Subgroups ◽  
Image Position

If $\unicode[STIX]{x1D703}$ is a subgroup property, a group $G$ is said to satisfy the double chain condition on $\unicode[STIX]{x1D703}$-subgroups if it admits no infinite double sequences $$\begin{eqnarray}\cdots <X_{-n}<\cdots <X_{-1}<X_{0}<X_{1}<\cdots <X_{n}<\cdots\end{eqnarray}$$ consisting of $\unicode[STIX]{x1D703}$-subgroups. We describe the structure of generalised radical groups satisfying the double chain condition on abelian subgroups.

Groups satisfying the double chain condition on non-abelian subgroups

2019 ◽  
Vol 19 (08) ◽  
pp. 2050145
Author(s):  
Mattia Brescia ◽  
Alessio Russo
Keyword(s):  
Chain Condition ◽  
Double Sequences ◽  
Property A ◽  
Double Chain ◽  
Abelian Subgroups

If [Formula: see text] is a subgroup property, a group [Formula: see text] is said to satisfy the double chain condition on [Formula: see text]-subgroups if it admits no infinite double sequences [Formula: see text] consisting of [Formula: see text]-subgroups. The structure of generalized radical groups satisfying the double chain condition on non-abelian subgroups is described.

scholarly journals On codes satisfying the double chain condition

1997 ◽  
Vol 175 (1-3) ◽  
pp. 173-195 ◽  
Author(s):  
Torleiv Kl∅ve
Keyword(s):  
Chain Condition ◽  
Double Chain

Groups satisfying the double chain condition on non-subnormal subgroups

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mattia Brescia
Keyword(s):  
Chain Condition ◽  
Double Sequences ◽  
Property A ◽  
Double Chain ◽  
Subnormal Subgroups

AbstractIf 𝜃 is a subgroup property, a group 𝐺 is said to satisfy the double chain condition on 𝜃-subgroups if it admits no infinite double sequences\cdots<X_{-n}<\cdots<X_{-1}<X_{0}<X_{1}<\cdots<X_{n}<\cdotsconsisting of 𝜃-subgroups. The structure of generalised radical groups satisfying the double chain condition on non-subnormal subgroups is described.

Groups satisfying the double chain condition on subnormal subgroups

2016 ◽  
Vol 65 (1) ◽  
pp. 255-261 ◽  
Author(s):  
Mattia Brescia ◽  
Francesco de Giovanni
Keyword(s):  
Chain Condition ◽  
Double Chain ◽  
Subnormal Subgroups

scholarly journals Reflexivity and adjustment strategies at the interfaces

Nordlyd ◽  
2011 ◽  
Vol 37 ◽  
pp. 119 ◽  
Author(s):  
Ismael Teomiro
Keyword(s):  
Chain Condition ◽  
Lexical Entry ◽  
Double Chain ◽  
Internal Argument ◽  
Reduction Operation ◽  
Adjustment Strategies ◽  
Reflexive Verbs ◽  
Semantic Element ◽  
Argument Reduction

<p>I argue in this work that Reinhart &amp; Reuland&rsquo;s (1993) conditions A and B hold for Spanish. I provide evidence supporting the hypothesis that this language makes use of both <strong>SE </strong>and <strong>SELF</strong>-anaphors. Inherent reflexive verbs undergo an internal argument reduction operation in the lexicon. However, the syntax always requires two arguments. Therefore certain clitics, which are SE-anaphors, are inserted in these derivations. This is a last-resort mechanism that makes an adjustment between the valence of the lexical entry of the verb and the requirements of the syntax in order for the derivation to converge at the C-I interface. These clitics are syntactic arguments. Nevertheless, they are not interpreted as semantic arguments since they violate the <em>double chain condition, </em>which forces nominal elements to share both a tense and thematic features with the verb and the tense heads. Non- inherent reflexive verbs require the presence of a SELF-anaphor, which is formed out of a SE-anaphor along with a protector SELF element. Therefore, both syntactic elements are interpreted as two distinguishable semantic elements at C-I despite the fact that there is binding between them both. The interpretation of both syntactic elements as just one semantic element is a pragmatic epiphenomenon.</p>

Slow Magnetization Relaxation in a 1-D Double-Chain Coordination Polymer Composed of {DyIII 4} Repeating Units

2013 ◽  
Vol 3 (2) ◽  
pp. 161-171 ◽  
Author(s):  
Dimitris Alexandropoulos ◽  
Chaoran Li ◽  
Catherine Raptopoulou ◽  
Vassilis Psycharis ◽  
Wolfgang Wernsdorfer ◽  
...  
Keyword(s):  
Coordination Polymer ◽  
Double Chain ◽  
Magnetization Relaxation

scholarly journals Double-Chain Cationic Surfactants: Swelling, Structure, Phase Transitions and Additive Effects

Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 3946
Author(s):  
Rui A. Gonçalves ◽  
Yeng-Ming Lam ◽  
Björn Lindman
Keyword(s):  
Phase Transitions ◽  
Phase Behaviour ◽  
Double Chain ◽  
Scanning Calorimetry ◽  
Alkyl Chains ◽  
X Ray Scattering ◽  
Amphiphilic Compounds ◽  
Liquid Phases ◽  
Lamellar Phases ◽  
Water Layers

Double-chain amphiphilic compounds, including surfactants and lipids, have broad significance in applications like personal care and biology. A study on the phase structures and their transitions focusing on dioctadecyldimethylammonium chloride (DODAC), used inter alia in hair conditioners, is presented. The phase behaviour is dominated by two bilayer lamellar phases, Lβ and Lα, with “solid” and “melted” alkyl chains, respectively. In particular, the study is focused on the effect of additives of different polarity on the phase transitions and structures. The main techniques used for investigation were differential scanning calorimetry (DSC) and small- and wide-angle X-ray scattering (SAXS and WAXS). From the WAXS reflections, the distance between the alkyl chains in the bilayers was obtained, and from SAXS, the thicknesses of the surfactant and water layers. The Lα phase was found to have a bilayer structure, generally found for most surfactants; a Lβ phase made up of bilayers with considerable chain tilting and interdigitation was also identified. Depending mainly on the polarity of the additives, their effects on the phase stabilities and structure vary. Compounds like urea have no significant effect, while fatty acids and fatty alcohols have significant effects, but which are quite different depending on the nonpolar part. In most cases, Lβ and Lα phases exist over wide composition ranges; certain additives induce transitions to other phases, which include cubic, reversed hexagonal liquid crystals and bicontinuous liquid phases. For a system containing additives, which induce a significant lowering of the Lβ–Lα transition, we identified the possibility of a triggered phase transition via dilution with water.

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