On wreath product of n-polygroups

2015 ◽  
Vol 14 (04) ◽  
pp. 1550060 ◽  
Author(s):  
S. Mirvakili ◽  
M. Farshi ◽  
B. Davvaz
Keyword(s):  
Wreath Product ◽  
Idempotent Element ◽  
Double Cosets ◽  
Isomorphism Theorems

In this paper, we shall introduce thin n-subpolygroups of a given n-polygroup and in this regards, the notion of wreath product of n-polygroups will be studied. Also, double cosets of n-polygroups are investigated and the classical isomorphism theorems of groups are generalized to n-polygroups. The main result of the paper is that a finite n-polygroup is singular if and only if it is a wreath product of n-subpolygroups all of which are thin or generated by an involution or by an idempotent element.

scholarly journals New extensions of polygroups by polygroups

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3655-3668
Author(s):  
Lumnije Shehu ◽  
Hani Khashan
Keyword(s):  
Wreath Product ◽  
Isomorphism Theorems

Extensions of polygroups such as direct hyper product and wreath product of polygroups have been introduced and studied earlier by Comer. In this paper, we define and study some other extensions. We first define regularly normal subpolygroups and prove that they induce quotient polygroup extensions. In addition, we prove that the kernel of every strong homomorphism is a regularly normal subpolygroup. This leads to new versions of the isomorphism theorems with respect to such subpolygroups. The main objective of the paper is to present a new extension K of a polygroup L by a polygroup H via the quotient polygroup H=I where I is regularly normal in H. This extension is a generalization of both the direct hyper product and the wreath product of polygroups.

scholarly journals Statistical Enumeration of Groups by Double Cosets

2021 ◽  
Author(s):  
Persi Diaconis ◽  
Mackenzie Simper
Keyword(s):  
Double Cosets

On fundamental isomorphism theorems in soft subgroups

2020 ◽  
Vol 24 (16) ◽  
pp. 11841-11851
Author(s):  
N. Çağman ◽  
R. Barzegar ◽  
S. B. Hosseini
Keyword(s):  
Isomorphism Theorems

On Commutator Length and Square Length of the Wreath Product of a Group by a Finitely Generated Abelian Group

2010 ◽  
Vol 17 (spec01) ◽  
pp. 799-802 ◽  
Author(s):  
Mehri Akhavan-Malayeri
Keyword(s):  
Abelian Group ◽  
Wreath Product ◽  
Finitely Generated ◽  
Commutator Length

Let W = G ≀ H be the wreath product of G by an n-generator abelian group H. We prove that every element of W′ is a product of at most n+2 commutators, and every element of W2 is a product of at most 3n+4 squares in W. This generalizes our previous result.

scholarly journals Computing Double Cosets in Soluble Groups

2001 ◽  
Vol 31 (1-2) ◽  
pp. 179-192 ◽  
Author(s):  
Michael C. Slattery
Keyword(s):  
Soluble Groups ◽  
Double Cosets

scholarly journals A note on Noetherian orders in Artinian rings

1979 ◽  
Vol 20 (2) ◽  
pp. 125-128 ◽  
Author(s):  
A. W. Chatters
Keyword(s):  
Noetherian Ring ◽  
Quotient Ring ◽  
Triangular Matrix ◽  
Idempotent Element ◽  
Noetherian Rings ◽  
Central Idempotent ◽  
Matrix Rings ◽  
Regular Elements ◽  
Zero Divisors ◽  
Left And Right

Throughout this note, rings are associative with identity element but are not necessarily commutative. Let R be a left and right Noetherian ring which has an Artinian (classical) quotient ring. It was shown by S. M. Ginn and P. B. Moss [2, Theorem 10] that there is a central idempotent element e of R such that eR is the largest Artinian ideal of R. We shall extend this result, using a different method of proof, to show that the idempotent e is also related to the socle of R/N (where N, throughout, denotes the largest nilpotent ideal of R) and to the intersection of all the principal right (or left) ideals of R generated by regular elements (i.e. by elements which are not zero-divisors). There are many examples of left and right Noetherian rings with Artinian quotient rings, e.g. commutative Noetherian rings in which all the associated primes of zero are minimal together with full or triangular matrix rings over such rings. It was shown by L. W. Small that if R is any left and right Noetherian ring then R has an Artinian quotient ring if and only if the regular elements of R are precisely the elements c of R such that c + N is a regular element of R/N (for further details and examples see [5] and [6]). By the largest Artinian ideal of R we mean the sum of all the Artinian right ideals of R, and it was shown by T. H. Lenagan in [3] that this coincides in any left and right Noetherian ring R with the sum of all the Artinian left ideals of R.

scholarly journals WREATH PRODUCTS, NILPOTENT ORBITS AND SYMPLECTIC DEFORMATIONS

2007 ◽  
Vol 18 (05) ◽  
pp. 473-481
Author(s):  
BAOHUA FU
Keyword(s):  
Wreath Product ◽  
Wreath Products ◽  
Nilpotent Orbit ◽  
Nilpotent Orbits ◽  
Symplectic Resolutions

We recover the wreath product X ≔ Sym 2(ℂ2/± 1) as a transversal slice to a nilpotent orbit in 𝔰𝔭6. By using deformations of Springer resolutions, we construct a symplectic deformation of symplectic resolutions of X.

Commutator Calculus for Wreath Product Groups

2015 ◽  
Vol 43 (5) ◽  
pp. 2152-2173
Author(s):  
Jeffrey M. Riedl
Keyword(s):  
Wreath Product

scholarly journals Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 321 ◽  
Author(s):  
Mehmet Çelik ◽  
Moges Shalla ◽  
Necati Olgun
Keyword(s):  
Group Theory ◽  
Significant Role ◽  
Classical Group ◽  
Algebraic Structures ◽  
Algebraic Systems ◽  
Homomorphism Theorem ◽  
Special Cases ◽  
Isomorphism Theorems

In classical group theory, homomorphism and isomorphism are significant to study the relation between two algebraic systems. Through this article, we propose neutro-homomorphism and neutro-isomorphism for the neutrosophic extended triplet group (NETG) which plays a significant role in the theory of neutrosophic triplet algebraic structures. Then, we define neutro-monomorphism, neutro-epimorphism, and neutro-automorphism. We give and prove some theorems related to these structures. Furthermore, the Fundamental homomorphism theorem for the NETG is given and some special cases are discussed. First and second neutro-isomorphism theorems are stated. Finally, by applying homomorphism theorems to neutrosophic extended triplet algebraic structures, we have examined how closely different systems are related.

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