<p style='text-indent:20px;'>In this paper, we propose to use a twisted dihedral group algebra for public-key cryptography. For this, introduce new <inline-formula><tex-math id="M1">\begin{document}$ 2 $\end{document}</tex-math></inline-formula>-cocycle id="M2">\begin{document}$ \alpha_{\lambda} $\end{document}</tex-math></inline-formula> twist the a...

We construct a new infinite family of four-dimensional isolated symplectic singularities with trivial local fundamental group, answering question Beauville raised in 2000. Three constructions are presented for this family: (1) as blowups the quotient C 4 $\mathbb {C}^4$ by dihedral group order 2 d $2d$ , (2) singular points Calogero–Moser spaces associated groups at equal parameters, and (3) ce...

Let k be an algebraically closed field of characteristic 2. We calculate the vertices of all indecomposable kD8-modules for the dihedral group D8 of order 8. We also give a conjectural formula of the induced module of a string module from kT0 to kG where G is a dihedral group G of order ≥ 8 and where T0 is a dihedral subgroup of index 2 of G. Some cases where we verified this formula are given.

One of the concepts in mathematics that developing rapidly today is Graph Theory. The development Theory has been combined with Group Theory, by representing a group graph. intersection graph from , noted whose vertices are all non-trivial subgroups and two distinct adjacent if only . In this research Dihedral group, we looking for shapes numerical invariants. results obtained then subgraphs gi...

For a given element $g$ of finite group $G$, the probablility that commutator randomly choosen pair elements in $G$ equals is relative commutativity degree $g$. In this paper we are interested studying Dihedral order $2n$ and Quaternion $2^{n}$ for any $n\geq 3$ examine infinite class Moufang Loops Chein type, $M(G,2)$.