we discuss whether finiteness properties of a profinite group $g$ can be deduced from the coefficients of the probabilisticzeta function $p_g(s)$. in particular we prove that if $p_g(s)$ is rational and all but finitely many non abelian composition factors of $g$ are isomorphic to $psl(2,p)$ for some prime $p$, then $g$ contains only finitely many maximal subgroups.

It has been recently observed that fundamental aspects of the classical theory factorization can be greatly generalized by combining languages monoids and preorders. This led to various theorems on existence certain factorizations, herein called ⪯-factorizations, for ⪯-non-units a (multiplicatively written) monoid H endowed with preorder ⪯, where an element u∈H is ⪯-unit if u⪯1H⪯u ⪯-non-unit ot...

We give upper bounds on the number of times the fixed point operator needs to be unfolded for strictness analysis of functional languages with lists. This extends previous work both in the syntax-directed nature of the approach and in the ability to deal with Wadler’s method for analysing lists. Limitations of the method are indicated.