We deene an invariant (M) of a nite volume hyperbolic 3-manifold M in the Bloch group B(C) and show it is determined by the simplex parameters of any degree one ideal triangulation of M. We show (M) lies in a subgroup of B(C) of nite Q-rank determined by the invariant trace eld of M. Moreover, the Chern-Simons invariant of M is determined modulo ra-tionals by (M). This leads to a simplicial for...

Let k be an imaginary quadratic number field with Ck,2, the 2-Sylow subgroup of its ideal class group Ck, of rank 4. We show that k has infinite 2-class field tower for particular families of fields k, according to the 4-rank of Ck, the Kronecker symbols of the primes dividing the discriminant ∆k of k, and the number of negative prime discriminants dividing ∆k. In particular we show that if the...

let $s$ be an ordered semigroup. a fuzzy subset of $s$ is anarbitrary mapping   from $s$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. in this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $s$ is introduced.regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.finally, two m...

background: cucumber mosaic virus (cmv) from the bromoviridae family, is one of the most widespread plant viruses in the world. objectives: in the present study tomato fields in guilan, isfahan, khorasan razavi, khuzestan and tehran provinces were surveyed to determine the presence of cmv subgroups during 2011-2012. materials and methods: out of 305 symptomatic leaf samples tested by enzyme-lin...

groups of infinite rank in which every subgroup is either normal or self-normalizing are characterized in terms of their subgroups of infinite rank.

abstract. in this paper we study some relations between the power andquotient power graph of a finite group. these interesting relations motivateus to find some graph theoretical properties of the quotient power graphand the proper quotient power graph of a finite group g. in addition, weclassify those groups whose quotient (proper quotient) power graphs areisomorphic to trees or paths.

a subgroup $x$ of a group $g$ is almost normal if the index $|g:n_g(x)|$ is finite, while $x$ is nearly normal if it has finite index in the normal closure $x^g$. this paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.

For an algebraic number field K with ring of integers $$\mathcal {O}_{K}$$ , important subgroup the ideal class group $$Cl_{K}$$ is Pólya group, denoted by Po(K), which measures failure -module $$Int(\mathcal {O}_{K})$$ integer-valued polynomials on from admitting a regular basis. In this paper, we prove that for any integer $$n \ge 2$$ there are infinitely many totally real bi-quadratic fields...

Background and Aim: There is a gap of information on the effect of time, disinfectant, and storage conditions on the dimensional stability of direct post patterns made of self-cure acrylic resins. This study assessed the effect of Deconex® and wet or dry stor-age conditions on the dimensional stability of post patterns made of Duralay and GC acrylic resins. Materials and Methods: Sixty spe...