Geodesic
Pseudocharacters on free groups, invariant with respect to some types of endomorphisms
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 2, pp. 167-176.

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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 $R=\tilde R*\prod_{i=k}^n\langle r_i \rangle$, 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. 
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     author = {D. Z. Kagan},
     title = {Pseudocharacters on free groups, invariant with respect to some types of endomorphisms},
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D. Z. Kagan. Pseudocharacters on free groups, invariant with respect to some types of endomorphisms. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 2, pp. 167-176. http://geodesic.mathdoc.fr/item/FPM_2012_17_2_a5/

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