We give a simple and unified proof showing that the unrestricted wreath product of weakly sofic, linear or hyperlinear group by an amenable is hyperlinear, respectively. By means Kaloujnine-Krasner theorem, this implies extensions with quotients preserve four aforementioned metric approximation properties. also discuss case co-amenable groups.

Defectless irreducible polynomials over a valued field (F, v) have been studied by means of strict systems of polynomial extensions and complete distinguished chains. Strong connections are developed here between these two approaches and applications made to both. In the tame case where a root α of an irreducible polynomial f generates a tamely ramified extension of (F, v), simple formulas are ...