<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...

The mol-ecule of the title compound, C(8)H(8)N(4)O(2), is nearly planar, with a dihedral angle between the rings of 1.1 (1)°. Adjacent mol-ecules are linked into a layered structure by hydr-oxy-oxo O-H⋯O and triazol-yl-hydr-oxy N-H⋯O hydrogen bonds. Only one of the H atoms of the pyramidal amino group is engaged in building up the infinite layer. The second H atom of the amino group also shows ...

In the structure of the title compound, C(14)H(12)ClNO, the ortho-Cl atom in the benzoyl ring is positioned syn to the C=O bond, while the meta-methyl group in the aniline ring is positioned anti to the N-H bond. The amide group forms dihedral angles of 60.1 (1) and 22.0 (1)°, respectively, with the benzoyl and aniline rings, while the angle between these rings is 38.7 (1)°. The crystal structu...

In the title compound, C(14)H(9)F(3)N(2)O, the best planes of the benzimidazole group and benzene ring form a dihedral angle of 26.68 (3)°. In the crystal, N-H⋯N hydrogen bonds link the mol-ecules into infinite chains parallel to the c axis. Stacking inter-actions between the benzimidazole groups [centroid-centroid distance = 3.594 (5) Å] assemble the mol-ecules into layers parallel to (100). T...

The conformations of the N-H and C=O bonds in the structure of the title compound, C(15)H(15)NO, are trans to each other. Furthermore, the position of the amide O atom is syn to the ortho-methyl group in the benzoyl ring. The central amide group is tilted at an angle of 59.96 (11)° to the benzoyl ring, and the benzoyl and aniline rings form a dihedral angle of 81.44 (5)°. N-H⋯O hydrogen bonds l...

a non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized fibonacci sequence , , , . a remarkable application of this definition may be find on the study of random covers in the cryptography. the 2-step generalized sequences for the dihedral groups studied for their pe...

In the title compound, C(10)H(8)N(3)S(+)·NO(3) (-)·H(2)O, one of the N atoms of the benzimidazole unit is protonated, unlike than that in the thia-zole group. This protonation leads to equalization of the bond angles at the two N atoms of the benzimidazole group. The benzimidazole and thia-zole systems are almost coplanar, forming a dihedral angle of 0.5 (2)°. In the crystal, the nitrate anion ...

in this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.