scholarly journals On the group matrices for a generalized dihedral group

1981 ◽  
Vol 39 ◽  
pp. 83-89 ◽  
Author(s):  
Kai Wang
Keyword(s):  
Dihedral Group ◽  
Group Matrices ◽  
Generalized Dihedral Group

The unit group of finite group algebra of a generalized dihedral group

2014 ◽  
Vol 07 (02) ◽  
pp. 1450034 ◽  
Author(s):  
Neha Makhijani ◽  
R. K. Sharma ◽  
J. B. Srivastava
Keyword(s):  
Finite Group ◽  
Group Theory ◽  
Finite Field ◽  
Group Algebra ◽  
Dihedral Group ◽  
Unit Group ◽  
Generalized Dihedral Group

Let [Formula: see text] be a generalized dihedral group of order 2n and 𝔽q be a finite field having q elements. In this note, we establish the structure of the unit group of [Formula: see text] for any odd n ≥ 3. This extends a result due to Kaur and Khan [Units in 𝔽2D2p, J. Algebra Appl. 13(2) (2014) 9pp., doi: 10.1142/S0219498813500904] as well as a result due to the authors [Units in 𝔽2kD2n, Int. J. Group Theory 3(3) (2014) 25–34].

scholarly journals On Minimal Distance-Regular Cayley Graphs of Generalized Dihedral Groups

10.37236/9755 ◽  
2020 ◽  
Vol 27 (4) ◽  
Author(s):  
Štefko Miklavič ◽  
Primož Šparl
Keyword(s):  
Closed Subset ◽  
Dihedral Group ◽  
Cayley Graphs ◽  
Complete Classification ◽  
Minimal Distance ◽  
Dihedral Groups ◽  
Generalized Dihedral Group

Let $G$ denote a finite generalized dihedral group with identity $1$ and let $S$ denote an inverse-closed subset of $G \setminus \{1\}$, which generates $G$ and for which there exists $s \in S$, such that $\langle S \setminus \{s,s^{-1}\} \rangle \ne G$. In this paper we obtain the complete classification of distance-regular Cayley graphs $\mathrm{Cay}(G;S)$ for such pairs of $G$ and $S$.

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 Resultants and group matrices

1980 ◽  
Vol 33 ◽  
pp. 111-122 ◽  
Author(s):  
Kai Wang
Keyword(s):  
Group Matrices

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).

Sign in / Sign up

Export Citation Format

Share Document