Automorphism groups of polycyclic-by-finite groups and arithmetic groups

We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construct examples of polycyclic-by-finite groups which have an automorphism group which does not contain an arithmetic group of finite index. Finally we discuss applications of our results to the groups of homotopy self-equivalences of K(\Gamma, 1)-spaces and obtain an extension of arithmeticity results of Sullivan in rational homotopy theory

How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition

This is an Accepted Manuscript of an article published by Taylor & Francis in Educational Psychologist on 16th January 2014, available online: http://wwww.tandfonline.com/10.1080/00461520.2013.865527The received view of mathematical practice is that mathematicians gain certainty in mathematical assertions by deductive evidence rather than empirical or authoritarian evidence. This assumption has influenced mathematics instruction where students are expected to justify assertions with deductive arguments rather than by checking the assertion with specific examples or appealing to authorities. In this paper, we argue that the received view about mathematical practice is too simplistic; some mathematicians sometimes gain high levels of conviction with empirical or authoritarian evidence and sometimes do not gain full conviction from the proofs that they read. We discuss what implications this might have, both for for mathematics instruction and theories of epistemic cognition

Discrete groups, analytic groups and Poincare series

SIGLEAvailable from British Library Document Supply Centre- DSC:D90338 / BLDSC - British Library Document Supply CentreGBUnited Kingdo