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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.
@article{ITA_2012__46_1_165_0,
author = {Silva, Pedro V.},
title = {Fixed points of endomorphisms of certain free products},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {165--179},
publisher = {EDP-Sciences},
volume = {46},
number = {1},
year = {2012},
doi = {10.1051/ita/2011125},
mrnumber = {2904968},
zbl = {1266.20069},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2011125/}
}
TY - JOUR AU - Silva, Pedro V. TI - Fixed points of endomorphisms of certain free products JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2012 SP - 165 EP - 179 VL - 46 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita/2011125/ DO - 10.1051/ita/2011125 LA - en ID - ITA_2012__46_1_165_0 ER -
%0 Journal Article %A Silva, Pedro V. %T Fixed points of endomorphisms of certain free products %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2012 %P 165-179 %V 46 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita/2011125/ %R 10.1051/ita/2011125 %G en %F ITA_2012__46_1_165_0
Silva, Pedro V. Fixed points of endomorphisms of certain free products. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 1, pp. 165-179. doi: 10.1051/ita/2011125
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