In the title pyrazole compound, C(21)H(15)N(3)O(4), an intra-molecular C-H⋯O hydrogen bond generates an S(7) ring motif. The essentially planar furan and pyrazole rings [maximum atomic deviations of 0.011 (2) and 0.006 (2) Å, respectively] make a dihedral angle of 9.21 (11)°. The nitro group is approximately coplanar with the attached furan ring, as indicated by the dihedral angle of 4.5 (2)°. ...

the order of the central of G must be finite and hence g is finite. That is, there is only a finite number of groups which contain a fixed number, greater than zero, of complete sets of non-invariant conjugate operators. From the theorem at the close of the preceding paragraph it results that there is an infinite number of groups such that each group contains one and only one complete set of no...

The title Mn(II) complex, [Mn(C(7)H(4)BrO(2))(2)(C(10)H(14)N(2)O)(2)(H(2)O)(2)], is centrosymmetric. The mol-ecule contains two 2-bromo-benzoate (BB) and two diethyl-nicotinamide (DENA) ligands and two water mol-ecules, all ligands being monodentate. The four O atoms in the equatorial plane around the Mn atom form a slightly distorted square-planar arrangement, while the distorted octa-hedral c...

In the centrosymmetric title complex, [Zn(C(7)H(4)BrO(2))(2)(C(10)H(14)N(2)O)(2)(H(2)O)(2)], the Zn(II) atom is located on an inversion center. The asymmetric unit contains one 2-bromo-benzoate (BB), one diethyl-nicotinamide (DENA) ligand and one coordinating water molecule. The four O atoms in the equatorial plane around the Zn atom form a slightly distorted square-planar arrangement, while th...

let $f_q d_{2n}$ be the group algebra of $d_{2n}$, the dihedral group of order $2n$ over $f_q=gf(q)$. in this paper, we establish the structure of $u(f_{2^k}d_{2n})$, the unit group of $f_{2^k}d_{2n}$ and that of its normalized unitary subgroup $v_*(f_{2^k}d_{2n})$ with respect to canonical involution $*$ when $n$ is odd.

This paper is inspired by the PQ penny flip game. It employs group-theoretic concepts to study original game and its possible extensions. In this paper, it shown that can be associated, in a precise way, with dihedral group D8 within there exist precisely two classes of equivalent winning strategies for Q. achieved proving are exactly different sequences states guarantee Q’s win probability 1.0...

the author studies the $bf r$$g$-module $a$ such that $bf r$ is an associative ring‎, ‎a group $g$ has infinite section $p$-rank (or infinite 0-rank)‎, ‎$c_{g}(a)=1$‎, ‎and for every‎ ‎proper subgroup $h$ of infinite section $p$-rank (or infinite 0-rank respectively) the quotient module $a/c_{a}(h)$ is‎ ‎a finite $bf r$-module‎. ‎it is proved that if the group $g$ under‎ ‎consideration is local...

In the mol-ecule of the title compound, C21H14N2O3, the quinazoline ring system [maximum deviation = 0.076 (1) Å] makes dihedral angles of 40.57 (9) and 42.31 (11)°, respectively, with the phenyl and 1,3-benzodioxole rings. The dihedral angle between the phenyl ring and the 1,3-benzodioxole ring is 4.34 (10)°. In the crystal, C-H⋯O hydrogen bonds link the mol-ecules into infinite zigzag chains ...