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Fixed points of endomorphisms of certain free products

Published online by Cambridge University Press:  23 November 2011

Pedro V. Silva
Pedro V. Silva*
Affiliation:
Centro de Matemática, Faculdade de Ciências, Universidade do Porto, R. Campo Alegre 687, 4169-007 Porto, Portugal. pvsilva@fc.up.pt
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Abstract

The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.

Keywords

Endomorphismsfixed pointsfree products
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 46 , Issue 1: Special issue dedicated to the 13th "Journées Montoises d'Informatique Théorique" , January 2012 , pp. 165 - 179
Copyright
© EDP Sciences 2011

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