K1 of Chevalley groups are nilpotent

Abstract Let F be a reduced irreducible root system and R be a commutative ring. Further, let G(F,R) be a Chevalley group of type F over R and E(F,R) be its elementary subgroup. We prove that if the rank of F is at least 2 and the Bass-Serre dimension of R is finite, then the quotient G(F,R)/E(F,R) is nilpotent by abelian. In particular, when G(F,R) is simply connected the quotient K1(F,R)=G(F,R)/E(F,R) is nilpotent. This result was previously established by Bak for the series A1 and by Hazrat for C1 and D1. As in the above papers we use the localisation-completion method of Bak, with some technical simplifications.

Space Science News: from archive to teaching resource, the secret life of newspapers

Worldwide, science education reform is aiming to promote 'scientific literacy' among young people. Typically, this is taken to include empowering them to engage critically with science in news media. This study explored the extent and nature of secondary science teachers' use of newspapers. It found that, though a great many use the resource, the majority do so incidentally and with the intention of showing the relevance of the subject rather than developing their students' criticality.

The Apperceptive Personality Test located in personality space.

The Apperceptive Personality Test is a projective test that claims to show good psychometric properties but which has not been related to the main, Eysenckian, personality traits. This study investigated the overlap between these two tests using a sample of students. Correlational and regression analyses showed a modest degree of overlap between Extraversion, Neuroticism and some of the scales from the Apperceptive Personality Test.