Pseudocharacters on a Class of Extensions of Free Groups

Abstract:

A {\it pseudocharacter\/} of a semigroup $S$ is a real function $\varphi$ on $S$ satisfying the following conditions.

1. The set $\{\varphi(xy)-\varphi(x)-\varphi(y) ;\;\; x,y\in S\} $ is bounded.
2. For $x\in S $ and $n\in \N$ (and $n\in \Z$ if $S$ is a group), \[\varphi(x^n)=n\varphi(x).\]

A description of the space of pseudocharacters on some extensions of free groups is given.

Tver State Agricultural Academy, Tver Sakharovo, Russia
Valeriy.Fayziev@tversu.ru