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 Fn 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 Fn, 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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