In the title compound, C(15)H(13)NO(2), all atoms of the carbazole group are coplanar (r.m.s. deviation = 0.005 Å), and the dihedral angle between this plane and C-O-C plane of oxane group is 57.1 (4)°. The crystal packing is stabilized by an N-H⋯O hydrogen bond, resulting in infinite supra-molecular chains along [001].

A group G is a CI-group with respect to graphs if two Cayley graphs of G are isomorphic if and only if they are isomorphic by a group automorphism of G. We show that an infinite family of groups which include Dn × F3p are not CI-groups with respect to graphs, where p is prime, n 6= 10 is relatively prime to 3p, Dn is the dihedral group of order n, and F3p is the nonabelian group of order 3p.

In this paper we classify fuzzy subgroups of the dihedral group $D_{pqrs}$  for distinct primes  $p$, $q$, $r$ and $s$. This follows similar work we have done on distinct fuzzy subgroups of some dihedral groups.We present formulae for the number of (i) distinct maximal chains of subgroups, (ii) distinct fuzzy subgroups and (iii) non-isomorphic classes of fuzzy subgroups under our chosen equival...

A new class of positive definite functions related to colour-length function on arbitrary Coxeter group is introduced. Extensions of positive definite functions, called the Riesz-Coxeter product, from the Riesz product on the Rademacher (Abelian Coxeter) group to arbitrary Coxeter group is obtained. Applications to harmonic analysis, operator spaces and noncommutative probability is presented. ...

Consider the cyclic group C2 of order two acting by complex-conjugation on the unit circle S1. The main result is that a finitely dominated manifold W of dimension> 4 admits a cocompact, free, discontinuous action by the infinite dihedral group D∞ if and only if W is the infinite cyclic cover of a free C2-manifold M such that M admits a C2-equivariant manifold approximate fibration to S1. The n...

Abstract. Let K be a differential field with algebraically closed field of constants C and G a linear algebraic group over C. We provide a characterization of the K-irreducible G-torsors for nonconnected groups G in terms of the first Galois cohomology H(K, G) and use it to construct Picard-Vessiot extensions which correspond to non-trivial torsors for the infinite quaternion group, the infinit...

In the crystal structure of the title compound, C(13)H(9)Cl(2)NO, the N-H and C=O bonds are anti to each other in the two independent mol-ecules. In one mol-ecule, the N-H bond is syn to the meta-chloro group of the attached ring; it is anti in the other mol-ecule. This relationship is also observed between the C=O bond and the meta-chloro substituent of its attached ring. The amide -NHCO- grou...

<p style='text-indent:20px;'>In this work, we present a matrix construction for reversible codes derived from skew dihedral group rings. By employing construction, the ring <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{F}_{j, k} $\end{document}</tex-math></inline-formula> and its associated Gray maps, show how one can construct of length id="M2">\...