A nilpotency criterion for derivations over reduced ℚ-algebras

2021 ◽  
pp. 1-11
Author(s):  
M’hammed El Kahoui ◽  
Najoua Essamaoui ◽  
Mustapha Ouali
Keyword(s):  
Reduced Ring ◽  
Locally Nilpotent

Let [Formula: see text] be a reduced ring containing [Formula: see text] and let [Formula: see text] be commuting locally nilpotent derivations of [Formula: see text]. In this paper, we give an algorithm to decide the local nilpotency of derivations of the form [Formula: see text], where [Formula: see text] are elements in [Formula: see text].

scholarly journals Certain locally nilpotent varieties of groups

2003 ◽  
Vol 67 (1) ◽  
pp. 115-119
Author(s):  
Alireza Abdollahi
Keyword(s):  
Prime Power ◽  
Power Exponent ◽  
Variety Of Groups ◽  
Periodic Groups ◽  
Locally Nilpotent

Let c ≥ 0, d ≥ 2 be integers and be the variety of groups in which every d-generator subgroup is nilpotent of class at most c. N.D. Gupta asked for what values of c and d is it true that is locally nilpotent? We prove that if c ≤ 2d + 2d−1 − 3 then the variety is locally nilpotent and we reduce the question of Gupta about the periodic groups in to the prime power exponent groups in this variety.

Groups with every subgroup ascendant-by-finite

2013 ◽  
Vol 11 (12) ◽  
Author(s):  
Sergio Camp-Mora
Keyword(s):  
Finite Group ◽  
Finite Index ◽  
Locally Finite Group ◽  
Locally Finite ◽  
Locally Nilpotent

AbstractA subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.

scholarly journals Emergence and Spread of kelch13 Mutations Associated with Artemisinin Resistance in Plasmodium falciparum Parasites in 12 Thai Provinces from 2007 to 2016

2018 ◽  
Vol 62 (4) ◽  
Author(s):  
Theerayot Kobasa ◽  
Eldin Talundzic ◽  
Rungniran Sug-aram ◽  
Patcharida Boondat ◽  
Ira F. Goldman ◽  
...  
Keyword(s):  
Plasmodium Falciparum ◽  
Gene Mutations ◽  
Artemisinin Resistance ◽  
Parasite Clearance ◽  
Resistance Mutations ◽  
Content Type ◽  
Artemisinin Derivatives ◽  
Reduced Ring ◽  
Control And Prevention ◽  
Greater Mekong Subregion

ABSTRACT Artemisinin-based combination therapy (ACT) is the most effective and widely used treatment for uncomplicated Plasmodium falciparum malaria and is a cornerstone for malaria control and prevention globally. Resistance to artemisinin derivatives has been confirmed in the Greater Mekong Subregion (GMS) and manifests as slow parasite clearance in patients and reduced ring stage susceptibility to artemisinins in survival assays. The P. falciparum kelch13 gene mutations associated with artemisinin-resistant parasites are now widespread in the GMS. We genotyped 277 samples collected during an observational study from 2012 to 2016 from eight provinces in Thailand to identify P. falciparum kelch13 mutations. The results were combined with previously reported genotyping results from Thailand to construct a map illustrating the evolution of P. falciparum kelch13 mutations from 2007 to 2016 in that country. Different mutant alleles were found in strains with different geographical origins. The artemisinin resistance-conferring Y493H and R539T mutations were detected mainly in eastern Thailand (bordering Cambodia), while P574L was found only in western Thailand and R561H only in northwestern Thailand. The C580Y mutation was found across the entire country and was nearing fixation along the Thai-Cambodia border. Overall, the prevalence of artemisinin resistance mutations increased over the last 10 years across Thailand, especially along the Thai-Cambodia border. Molecular surveillance and therapeutic efficacy monitoring should be intensified in the region to further assess the extent and spread of artemisinin resistance.

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