Let X be a complete simplicial toric variety over a finite field Fq with homogeneous coordinate ring S = Fq[x1, . . . , xr] and split torus TX ∼= (Fq). We prove that vanishing ideal of a subset Y of the torus TX is a lattice ideal if and only if Y is a subgroup. We show that these subgroups are exactly those subsets that are parameterized by Laurents monomials. We give an algorithm for determin...

in this paper, we extend the construction of a fuzzy subgroup generated by a fuzzy subset to $l$-setting. this construction is illustrated by an example. we also prove that for an $l$-subset of a group, the subgroup generated by its level subset is the level subset of the subgroup generated by that $l$-subset provided the given $l$-subset possesses sup-property.

Suppose that P is a convex polyhedron in the hyperbolic 3-space with finite volume and P has integer ( > 1) submultiples of it as dihedral angles. We prove that if the rank of the abelianization of a normal torsion-free finite index subgroup of the polyhedral group G associated to P is one, then P has exactly one ideal vertex of type (2,2,2,2) and G has an index two subgroup which does not cont...

In papers by Semmes [6], Macpherson and Neumann [4] and Brazil, Covington, Penttila, Praeger and Woods [2], it has been shown that stabilizers of filters (equivalently, stabilizers of ideals) play a crucial role in the study of maximal subgroups of infinite symmetric groups. Semmes proved that if if is a maximal subgroup of S = Sym (Q), where Q is a set of infinite cardinality K and H contains ...

let $g$ be a finite group‎. ‎a subgroup‎ ‎$h$ of $g$ is called an $mathcal h $ -subgroup in‎ ‎$g$ if $n_g (h)cap h^gleq h$ for all $gin‎ ‎g$. a subgroup $h$ of $g$ is called a weakly‎ $mathcal h^ast $-subgroup in $g$ if there exists a‎ ‎subgroup $k$ of $g$ such that $g=hk$ and $hcap‎ ‎k$ is an $mathcal h$-subgroup in $g$. we‎ ‎investigate the structure of the finite group $g$ under the‎ ‎assump...

Definition 3.4. The ideal group IA of a noetherian domain A is the group of invertible fractional ideals. Note that, despite the name, elements of IA need not be ideals. Every nonzero principal fractional ideal (x) is invertible (since (x)−1 = (x−1)), and a product of principal fractional ideals is principal (since (x)(y) = (xy)), as is the unit ideal (1), thus the set of nonzero principal frac...

For a given integer n, we provide some families of imaginary quadratic number fields the form Q(4q2−pn), whose ideal class group has subgroup isomorphic to Z/nZ.

purpose: in the present study we have tried to find the most reliable intraocular lens (iol) power calculation formula in patients with keratoconus (kcn) and cataract. methods: in a prospective case series between october 2010 and march 2012, eligible patients with cataract and kcn underwent phacoemulsification with iol implantation. preoperatively, based on iol master keratometric data iol pow...

a subgroup $h$ is said to be $nc$-supplemented in a group $g$ if there exists a subgroup $kleq g$ such that $hklhd g$ and $hcap k$ is contained in $h_{g}$, the core of $h$ in $g$. we characterize the supersolubility of finite groups $g$ with that every maximal subgroup of the sylow subgroups is $nc$-supplemented in $g$.

suppose that $h$ is a subgroup of $g$‎, ‎then $h$ is said to be‎ ‎$s$-permutable in $g$‎, ‎if $h$ permutes with every sylow subgroup of‎ ‎$g$‎. ‎if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|‎, ‎|h|)=1$)‎, ‎then $h$ is called an $s$-semipermutable subgroup of $g$‎. ‎in this paper‎, ‎we say that $h$ is partially $s$-embedded in $g$ if‎ ‎$g$ has a normal subgroup $t$ such that $ht...