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Inverse automata and profinite topologies on a free group

✍ Scribed by Benjamin Steinberg

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 169 KB
Volume: 167
Category: Article
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(01)00030-5

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✦ Synopsis

This paper gives an elementary, self-contained proof that a ÿnite product of ÿnitely generated subgroups of a free group is closed in the proÿnite topology. The proof uses inverse automata (graph immersions) and inverse monoid theory. Generalizations are given to other topologies. In particular, we obtain the new result that, for arborescent pseudovarieties, the product of two closed ÿnitely generated subgroups is again closed. An application to monoid theory is given.

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