Limits over categories of extensions

We consider limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. We also discuss higher (or derived) limits over categories of extensions.Comment: 18 page

Lie Dimension Subrings

We compare, for L a Lie ring over the integers, its lower central series (\gamma_n(L))_{n>0} and its dimension series defined by \delta_n(L):=L\cap \varpi^n(L) in the universal enveloping algebra of L. We show that \gamma_n(L)=\delta_n(L) for all n<4, but give an example showing that they may differ if n=4. We introduce simplicial methods to describe these results, and to serve as a possible tool for further study of the dimension series.Comment: Small typos fixed wrt v

Inspection and crime prevention : an evolutionary perspective

In this paper, we analyse inspection games with an evolutionary perspective. In our evolutionary inspection game with a large population, each individual is not a rational payoff maximiser, but periodically updates his strategy if he perceives that other individuals' strategies are more successful than his own, namely strategies are subject to the evolutionary pressure. We develop this game into a few directions. Firstly, social norms are incorporated into the game and we analyse how social norms may influence individuals' propensity to engage in criminal behaviour. Secondly, a forward-looking inspector is considered, namely, the inspector chooses the level of law enforcement whilst taking into account the effect that this choice will have on future crime rates. Finally, the game is extended to the one with continuous strategy spaces

Automorphisms of abelian group extensions

Let $1 \to N \to G \to H \to 1$ be an abelian extension. The purpose of this paper is to study the problem of extending automorphisms of $N$ and lifting automorphisms of $H$ to certain automorphisms of $G$.Comment: 11 page