We clarify the explicit structure of the Hurwitz quaternion order, which is of fundamental importance in Riemann surface theory and systolic geometry. We present some properties of the associated congruence subgroups. Namely, we show that a Hurwitz group defined by a congruence subgroup associated with an odd ideal, is necessarily defined by a principal congruence subgroup. All such Hurwitz gro...

OBJECTIVE To assess the efficacy of probiotic Lactobacillus on serum lipids using a meta-analysis of randomized, controlled trials. METHODS Fifteen studies containing 15 trials, with 976 subjects were included. The pooled WMD was calculated by random effects model. RESULTS Probiotic Lactobacillus consumption significantly reduced TC by 0.26mmol/l (95% CI, -0.40 to -0.12) and LDL-C by 0.23mm...

Let G be a finite subgroup of a symplectic group Sp2d(Ql). Despite the fact ([3]) that G can fail to be conjugate in GL2d(Ql) to a subgroup of Sp2d(Zl), we prove that it can nevertheless be embedded in Sp2d(Fl) in such a way that the characteristic polynomials are preserved (mod l), as long as l > 3. We start with the following “rigidity” result, which is in the spirit of similar results by Min...

The non-split extension group $overline{G} = 5^3{^.}L(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in Ly. The group $overline{G}$ in turn has L(3,5) and $5^2{:}2.A_5$ as inertia factors. The group $5^2{:}2.A_5$ is of order 3 000 and is of index 124 in L(3,5). The aim of this paper is to compute the Fischer-Clifford matrices of $overline{G}$, which together with associated parti...

We present a function F for each simple real linear Lie group G with real rank at least 2 such that F bounds from above all the K-matrix coeecients of non-trivial irreducible spherical unitary representations of G where K is a maximal compact subgroup of G. This enables us to determine when a closed subgroup H is a (G; K)-tempered subgroup of G: for example, if the restriction Fj H of F to H li...

Sequence analysis was performed of all or part of the genes encoding the fusion (F), polymerase (L) and attachment (G) proteins of two French non-A/non-B avian pneumovirus (APV) isolates (Fr/85/1 and Fr/85/2). The two isolates shared at least 99.7% nt and 99.0% aa sequence identity. Comparison with the F genes from subgroup A, subgroup B or Colorado APVs revealed nt and aa identities of 70.0-80...

We prove a new uniform bound for subgroup growth of a Chevalley group G over the local ring F[[t]] and also over local pro-p rings of higher Krull dimension. This is applied to the determination of congruence subgroup growth of arithmetic groups over global fields of positive characteristic. In particular, we show that the subgroup growth of SLn(Fp[t]) (n ≥ 3) is of type nlog n . This was one o...

Many studies have investigated the lattice structure of fuzzy substructures of algebraic sets such as group and ring. Some important results about modularity and distributivity have been obtained in these studies. In this paper, we first define the notion of (normal) (λ,μ)-L-subgroups on a group and investigate some of their properties. In particular, we discuss the relationships among ordinary...

we call $h$ an $ss$-embedded subgroup of $g$ if there exists a‎ ‎normal subgroup $t$ of $g$ such that $ht$ is subnormal in $g$ and‎ ‎$hcap tleq h_{sg}$‎, ‎where $h_{sg}$ is the maximal $s$-permutable‎ ‎subgroup of $g$ contained in $h$‎. ‎in this paper‎, ‎we investigate the‎ ‎influence of some $ss$-embedded subgroups on the structure of a‎ ‎finite group $g$‎. ‎some new results were obtained.