Rational codes and free profinite monoids

• Type: Article in International Scientific Journal
• Date: 2009

Authors

Jorge Almeida (Author) FCUP; Benjamin Steinberg (Author) Other

Journal

Title: Journal of the London Mathematical Society

Vol. 79

Pages: 465-477

ISSN: 0024-6107

Publisher: Wiley-Blackwell

Indexing

ISI Web of Knowledge - 3 Citations

Scopus - 2 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-003-M8B

DOI: 10.1112/jlms/jdn083

Abstract (EN): It is well known that clopen subgroups of finitely generated free profinite groups are again finitely generated free profinite groups. Clopen submonoids of free profinite monoids need not be finitely generated nor free. Margolis, Sapir and Weil proved that the closed submonoid generated by a finite code (which is, in fact, clopen) is a free profinite monoid generated by that code. In this note we show that a clopen submonoid is free profinite if and only if it is the closure of a rational free submonoid. In this case its unique closed basis is clopen, and is, in fact, the closure of the corresponding rational code. More generally, our results apply to free pro-H monoids for H an extension-closed pseudovariety of groups.

Language: English

Type (Professor's evaluation): Scientific