On the Order of Polynilpotent Multipliers of Some Nilpotent Products of Cyclic pp-Groups

In this article we show that if ${\cal V}$ is the variety of polynilpotent groups of class row $(c_1,c_2,...,c_s),\ {\mathcal N}_{c_1,c_2,...,c_s}$, and $G\cong{\bf {Z}}_{p^{\alpha_1}}\stackrel{n}{*}{\bf {Z}}_{p^{\alpha_2}}\stackrel{n}{*}...\stackrel{n}{*}{\bf{Z}}_{p^{\alpha_t} }$ is the $n$th nilpotent product of some cyclic $p$-groups, where $c_1\geq n$, $\alpha_1 \geq \alpha_2 \geq...\geq \alpha_t$ and $(q,p)=1$ for all primes $q$ less than or equal to $n$, then $|{\mathcal N}_{c_1,c_2,...,c_s}M(G)|=p^{d_m}$ if and only if $G\cong{\bf {Z}}_{p}\stackrel{n}{*}{\bf {Z}}_{p}\stackrel{n}{*}...\stackrel{n}{*}{\bf{Z}}_{p }$ ($m$-copies), where $m=\sum _{i=1}^t \alpha_i$ and $d_m=\chi_{c_s+1}(...(\chi_{c_2+1}(\sum_{j=1}^n \chi_{c_1+j}(m)))...)$. Also, we extend the result to the multiple nilpotent product $G\cong{\bf {Z}}_{p^{\alpha_1}}\stackrel{n_1}{*}{\bf {Z}}_{p^{\alpha_2}}\stackrel{n_2}{*}...\stackrel{n_{t-1}}{*}{\bf{Z}}_{p^{\alpha_t} }$, where $c_1\geq n_1\geq...\geq n_{t-1}$. Finally a similar result is given for the $c$-nilpotent multiplier of $G\cong{\bf {Z}}_{p^{\alpha_1}}\stackrel{n}{*}{\bf {Z}}_{p^{\alpha_2}}\stackrel{n}{*}...\stackrel{n}{*}{\bf{Z}}_{p^{\alpha_t}}$ with the different conditions $n \geq c$ and $(q,p)=1$ for all primes $q$ less than or equal to $n+c.$Comment: 10 page

The prevalence of gestational diabetes mellitus and its related risk factors in Gorgan, north of Iran. Selective or universal screening test is cost-effective?

Gestational diabetes mellitus (GDM) is the most prevalent metabolic disorder in pregnancy. GDM is defined in <1 % to 28 % of pregnancies, depending on the diagnostic criteria, the ethnic and racial characteristics. This study was performed to determine the prevalence of GDM and related risk factors among pregnant women in Gorgan, north of Iran. In a cross sectional study, 1276 pregnant women were recruited. All of women screened with glucose challenge test (GCT) in 24–28th wks of gestational age. Women with positive GCT underwent 100 g glucose tolerance test (OGTT). Diagnosis of GDM was according to Carpenter and Coustan’s criteria. GCT was positive in 200 women (15.8 % with CI: 13.8 %–17.8 %) and GDM was diagnosed in 62 case (4.9 % with CI:3.7 %–6.8 %). In a multiple logistic regression, risk factors such as age, BMI, history of macrosomia, familial history of diabetes and impaired fasting glucose (IFG) were identified as independent risk factors for GDM (p < 0.05). Among GDM cases, 3.2 %(2 women) had no risk factor. These results show moderate prevalence of GDM in north of Iran. It seems that a selective GDM screening method for women with some risk factors is more appropriate than general screening. © 2015, Research Society for Study of Diabetes in India