Several theoretical studies have suggested that large samples of randomly ascertained siblings can be efficiently used to ascertain phenotypically extreme individuals and increase power to detect genetic linkage. Phenotypes that can be reliably measured by questionnaire are of obvious utility for such selection strategies, as large numbers of individuals can be contacted without laborious individual interview. As the first step in developing a large randomly-ascertained family cohort in southwest England, a sample of 88 000 individuals, including more than 34 000 sibling pairs in 20 000 sibships, was administered the Eysenck Personality Questionnaire (EPQ) by commercial mailing. The sample age ranges were 20–67 years and comprised 59% males and 41% females. Descriptive properties of the EPQ scales are similar to those reported from other large family cohorts. Test–retest correlations on 1681 probands in the sample are substantial for the N-scale (r = 0.93), but somewhat more modest for the other scales (range r = 0.70–0.88). Phenotypic and sibling correlations correspond quite closely to those of twin studies. Twin Research (2000) 3, 310–315.

We find a lower bound on the number of imaginary quadratic extensions of the function field ${{\mathbb{F}}_{q}}\left( T \right)$ whose class groups have an element of a fixed order.

More precisely, let $q\,\ge \,5$ be a power of an odd prime and let $g$ be a fixed positive integer $\ge \,3$. There are $\gg \,{{q}^{\ell \left( \frac{1}{2}+\frac{1}{g} \right)}}$ polynomials $D\,\in \,{{\mathbb{F}}_{q}}\left[ T \right]$ with $\deg \left( D \right)\,\le \,\ell $ such that the class groups of the quadratic extensions ${{\mathbb{F}}_{q}}\left( T,\,\sqrt{D} \right)$ have an element of order $g$.