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New York Journal of Mathematics 6 (2000), 135-152.

Pseudocharacters on a Class of Extensions of Free Groups

Valeriy Fayziev

Published: September 12, 2000
Keywords: Free group, extension of free groups, quasicharacter, pseudocharacter, linear space
Subject: 20F99, 39B62, 39B82


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.

Author information:
Tver State Agricultural Academy, Tver Sakharovo, Russia