scholarly journals On a Non-Abelian Variety of Groups which are Symmetric Algebras.

1994 ◽  
Vol 74 ◽  
pp. 184
Author(s):  
Ernest Plonka
Keyword(s):  
Abelian Variety ◽  
Symmetric Algebras ◽  
Variety Of Groups

Chains of Varieties

1974 ◽  
Vol 26 (1) ◽  
pp. 190-206 ◽  
Author(s):  
Narain Gupta ◽  
Frank Levin ◽  
Akbar Rhemtulla
Keyword(s):  
Abelian Variety ◽  
Variety Of Groups

SummaryIf is a variety of groups that can be denned by n-variable laws and (m) is the variety all of whose m-generator groups are in then there corresponds the chain: (1) ≧ (2) ≧ . . . ≧ (n) = . In this paper such chains are investigated to determine which of the inclusions are proper for certain varieties . In particular the inclusions are shown to be all proper for the varieties where is the variety of nilpotent-of-class-c groups, is the abelian variety and is the variety of centre-bymetabelian groups. For the inclusions are likewise proper but for the corresponding chain is:

scholarly journals Logical stability in group theory

1976 ◽  
Vol 21 (3) ◽  
pp. 267-276 ◽  
Author(s):  
J. T. Baldwin ◽  
Jan Saxl
Keyword(s):  
Group Theory ◽  
Abelian Variety ◽  
Variety Of Groups ◽  
Locally Nilpotent

AbstractThis paper investigates the logical stability of various groups. Theorem 1: If a group G is stable and locally nilpotent then it is solvable. Theorem 2: Every non-Abelian variety of groups is unstable.

scholarly journals Natural dualities for dihedral varieties

1996 ◽  
Vol 61 (2) ◽  
pp. 216-228 ◽  
Author(s):  
B. A. Davey ◽  
R. W. Quackenbush
Keyword(s):  
Abelian Variety ◽  
Natural Duality ◽  
Variety Of Groups

AbstractA strong, natural duality is established for the variety by a dihedral gruop of order 2m with m odd. This is the first natural duality for a non-abelian variety of groups.

scholarly journals On the lattice of varieties of completely regular semigroups

1983 ◽  
Vol 35 (2) ◽  
pp. 227-235 ◽  
Author(s):  
P. R. Jones
Keyword(s):  
Lattice Of Varieties ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Variety Of Groups ◽  
Completely Regular Semigroups ◽  
Subdirect Products

AbstractSeveral morphisms of this lattice V(CR) are found, leading to decompostions of it, and various sublattices, into subdirect products of interval sublattices. For example the map V → V ∪ G (where G is the variety of groups) is shown to be a retraction of V(CR); from modularity of the lattice V(BG) of varieties of bands of groups it follows that the map V → (V ∪ V V G) is an isomorphism of V(BG).

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.

Tengku Mahmud Mahyiddeen and the Dilemma of Partisan Duality

1992 ◽  
Vol 23 (1) ◽  
pp. 37-59 ◽  
Author(s):  
Hugh Wilson
Keyword(s):  
United Kingdom ◽  
Independent State ◽  
The United Kingdom ◽  
Variety Of Groups ◽  
Peace Settlement

Lingering recollections of Pattani's proud tradition as an independent state were crystallized into a popular desire for the separation of the predominantly Malay Southern Provinces from Thailand, largely as a result of the aggressively nationalistic policies of Phibul Songkhram's wartime administration; when the war ended, widely circulated rumours encouraged Malays in the area to believe that the United Kingdom intended to annex the region to British Malaya as part of a peace settlement. Although this hope was dashed by the Agreement between the two countries of January 1, 1946, the idea of separation from Thailand continued to provide a goal towards which a variety of groups struggled by means ranging from polemics to sporadic acts of violence.

PBW deformations of quantum symmetric algebras and their group extensions

2016 ◽  
Vol 15 (03) ◽  
pp. 1650049 ◽  
Author(s):  
Piyush Shroff ◽  
Sarah Witherspoon
Keyword(s):  
Finite Group ◽  
Lie Algebra ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Group Extensions ◽  
Enveloping Algebra ◽  
Symmetric Algebras ◽  
Necessary And Sufficient ◽  
Special Case

We examine PBW deformations of finite group extensions of quantum symmetric algebras, in particular the quantum Drinfeld orbifold algebras defined by the first author. We give a homological interpretation, in terms of Gerstenhaber brackets, of the necessary and sufficient conditions on parameter functions to define a quantum Drinfeld orbifold algebra, thus clarifying the conditions. In case the acting group is trivial, we determine conditions under which such a PBW deformation is a generalized enveloping algebra of a color Lie algebra; our PBW deformations include these algebras as a special case.

The quasi-variety of groups with trivial fourth dimension subgroup

2006 ◽  
Vol 9 (3) ◽  
Author(s):  
Roman Mikhailov ◽  
Inder Bir S Passi
Keyword(s):  
Fourth Dimension ◽  
Variety Of Groups
Sign in / Sign up

Export Citation Format

Share Document