Lattice Definition. (Lattice) Given n linearly independent vectors b1, , bn ∈ R, the lattice generated by them · · · is defined as L(b1, b2, · · · bn) = { xibi|xi ∈ Z}. We refer to b1, · · · , bn as a basis of the lattice. Equivalently, if we define B as the m × n matrix whose columns are b1, , bn, then the lattice generated by B is · · · L(B) = L(b1, b2, · · · , bn) = {Bx|x ∈ Z}. We say that t...

For a number field K, we show that any S-arithmetic subgroup of SL2(K) contains a subgroup of finite index generated by three elements if card(S) ≥ 2.

A subgroup Q of a group G is commensurated if the commensurator of Q in G is the entire group G. Our main result is that a finitely generated group G containing an infinite, finitely generated, commensurated subgroup H, of infinite index in G is 1-ended and semistable at ∞. If additionally, Q and G are finitely presented and either Q is 1-ended or the pair (G,Q) has 1 filtered end, then G is si...

We study orbit codes in the field extension $ \mathbb{F}_{q^n} $. First we show that automorphism group of a cyclic code is contained normalizer Singer subgroup if generated by subspace not proper subfield then generalize to orbits under subgroup. In situation some exceptional cases arise and open remain. Finally characterize linear isometries between such codes.

The K-theory of the title is described in terms of the Ktheory of finite subgroups, as generalized sheaf homology of a quotient space. A corollary is that if G is torsion-free, then the Whitehead groups Wh t(ZG) vanish for all i. 1. The main result. Suppose that G is a poly-(finite or cyclic) group. Then there is a virtually connected and solvable Lie group L that contains G as a discrete cocom...

We report here the molecular cloning of new members of the penaeidin family from two Atlantic penaeids from Brazil, Litopenaeus schmitti and Farfantepenaeus paulensis. The presence of penaeidins in the granular hemocytes of both shrimps was first evidenced by immunofluorescence, using polyclonal antibodies raised against L. vannamei penaeidin Litvan PEN3-1. cDNAs from the hemocytes of both Braz...

The expression of immune response as a leukocytic infiltrate by CD4+ and CD8+ cells in the epithelium and in the intestinal lamina propria of chicks fed Lactobacillus spp or cecal microflora (CM) and experimentally challenged or not with Salmonella enterica serovar Enteritidis (SE) was studied using immunohistochemistry. Three hundred and twenty dayof-hatch broiler chicks were divided into four...

A celebrated theorem of Marshall Hall Jr. implies that finitely generated free groups are subgroup separable and that all of their finitely generated subgroups are retracts of finite-index subgroups. We use topological techniques inspired by the work of Stallings to prove that all limit groups share these two properties. This answers a question of Sela. Limit groups are finitely presented group...

The aim of this paper is to describe the structure finitely generated subgroups a family branch groups, which includes first Grigorchuk group and Gupta-Sidki 3-group. This description made via notion block subgroup. We then use show that all groups in above are subgroup separable (LERF). These results obtained as corollary more general structural statement on subdirect products just infinite gr...

If G is a group with supersimple theory having finite SU -rank, the subgroup of G generated by all of its normal nilpotent subgroups is definable and nilpotent. This answers a question asked by Elwes, Jaligot, Macpherson and Ryten in [5]. If H is any group with supersimple theory, the subgroup of H generated by all of its normal soluble subgroups is definable and soluble.