Fixed points of endomorphisms of certain free products
Centro de Matemática, Faculdade de Ciências, Universidade do
Porto, R. Campo Alegre
Accepted: 3 October 2011
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.
Mathematics Subject Classification: 20M05 / 20F10
Key words: Endomorphisms / fixed points / free products
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