FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 2, PAGES 167-176

**Pseudocharacters on free groups, invariant with respect to some types
of endomorphisms**

D. Z. Kagan

Abstract

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We investigate methods for constructing nontrivial pseudocharacters
on free group $F$_{n} invariant
with respect to certain types of endomorphisms.
We find some conditions for endomorphisms of the free group under
which there is a nontrivial pseudocharacter that is invariant
with respect to these endomorphisms.
We consider free products $\$\; R\; =\; \backslash tilde\; R\; *\; \backslash prod\_\{i=k\}^n\; \backslash langle\; r\_i\; \backslash rangle\; \$$, where
one factor is $F$_{n}, and the
other factor is a group on which there is a pseudocharacter.
For such products we obtain a similar result about the conditions
of existence of nontrivial pseudocharacters invariant with respect to
certain endomorphisms.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k112/k11206h.htm

Last modified: March 6, 2012