A MINIMAL CONGRUENCE LATTICE REPRESENTATION FOR

2020 ◽  
Vol 108 (3) ◽  
pp. 332-340
Author(s):  
ROGER BUNN ◽  
DAVID GROW ◽  
MATT INSALL ◽  
PHILIP THIEM
Keyword(s):  
Congruence Lattice ◽  
Dihedral Group ◽  
Unary Algebra ◽  
Left Translation ◽  
Lattice Representation

Let $p$ be an odd prime. The unary algebra consisting of the dihedral group of order $2p$, acting on itself by left translation, is a minimal congruence lattice representation of $\mathbb{M}_{p+1}$.

scholarly journals Some characterizatsion of coprime graph of dihedral group D 2n

2021 ◽  
Vol 1722 ◽  
pp. 012051
Author(s):  
A G Syarifudin ◽  
Nurhabibah ◽  
D P Malik ◽  
I G A W Wardhana
Keyword(s):  
Dihedral Group ◽  
Group D

scholarly journals Three-state quantum walk on the Cayley Graph of the Dihedral Group

2021 ◽  
Vol 20 (3) ◽  
Author(s):  
Ying Liu ◽  
Jia-bin Yuan ◽  
Wen-jing Dai ◽  
Dan Li
Keyword(s):  
Cayley Graph ◽  
Dihedral Group ◽  
Quantum Walk

scholarly journals A note on central group extensions

1973 ◽  
Vol 15 (4) ◽  
pp. 428-429 ◽  
Author(s):  
G. J. Hauptfleisch
Keyword(s):  
Abelian Group ◽  
Homomorphic Image ◽  
Free Group ◽  
Central Extension ◽  
Dihedral Group ◽  
Group Extension ◽  
Central Group ◽  
Group Extensions

If A, B, H, K are abelian group and φ: A → H and ψ: B → K are epimorphisms, then a given central group extension G of H by K is not necessarily a homomorphic image of a group extension of A by B. Take for instance A = Z(2), B = Z ⊕ Z, H = Z(2), K = V4 (Klein's fourgroup). Then the dihedral group D8 is a central extension of H by K but it is not a homomorphic image of Z ⊕ Z ⊕ Z(2), the only group extension of A by the free group B.

scholarly journals Strong duality for metacyclic groups

2002 ◽  
Vol 73 (3) ◽  
pp. 377-392 ◽  
Author(s):  
R. Quackenbush ◽  
C. S. Szabó
Keyword(s):  
Finite Group ◽  
Dihedral Group ◽  
Strong Duality ◽  
Sylow Subgroups ◽  
Metacyclic Groups ◽  
Group D

AbstractDavey and Quackenbush proved a strong duality for each dihedral group Dm with m odd. In this paper we extend this to a strong duality for each finite group with cyclic Sylow subgroups (such groups are known to be metacyclic).

scholarly journals On representing Mn's by congruence lattice of finite algebras

1983 ◽  
Vol 44 (3) ◽  
pp. 299-308 ◽  
Author(s):  
M.G. Stone ◽  
R.H. Weedmark
Keyword(s):  
Congruence Lattice ◽  
Finite Algebras
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