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Published: 
September 12, 2000

Keywords: 
Free group, extension of free groups, quasicharacter, pseudocharacter, linear space

Subject: 
20F99, 39B62, 39B82

Abstract:

A {\it pseudocharacter\/} of a
semigroup $S$ is a real function $\varphi$ on $S$
satisfying the following conditions.
 The set $\{\varphi(xy)\varphi(x)\varphi(y) ;\;\; x,y\in S\} $ is
bounded.
 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.

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