Images of locally nilpotent derivations of polynomial algebras in three variables

2021 ◽  
Vol 569 ◽  
pp. 401-415
Author(s):  
Xiaosong Sun ◽  
Dayan Liu
Keyword(s):  
Polynomial Algebras ◽  
Locally Nilpotent

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.

scholarly journals Gelfand-Kirillov Dimensions of Modules over Differential Difference Algebras

2016 ◽  
Vol 23 (04) ◽  
pp. 701-720 ◽  
Author(s):  
Xiangui Zhao ◽  
Yang Zhang
Keyword(s):  
Computational Method ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Polynomial Algebras ◽  
Ore Extensions ◽  
Basis Method ◽  
Finitely Generated Modules ◽  
Kirillov Dimension

Differential difference algebras are generalizations of polynomial algebras, quantum planes, and Ore extensions of automorphism type and of derivation type. In this paper, we investigate the Gelfand-Kirillov dimension of a finitely generated module over a differential difference algebra through a computational method: Gröbner-Shirshov basis method. We develop the Gröbner-Shirshov basis theory of differential difference algebras, and of finitely generated modules over differential difference algebras, respectively. Then, via Gröbner-Shirshov bases, we give algorithms for computing the Gelfand-Kirillov dimensions of cyclic modules and finitely generated modules over differential difference algebras.

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.

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