On the groups of codes with empty kernel.
type: Item
instance of: scholarly article
title: On the groups of codes with empty kernel.
zbMATH Open document ID: 1202.20071
author: Jean Berstel
author: Clelia De Felice
author: Dominique Perrin
author: Giuseppina Rindone
published in: Semigroup Forum
publication date: 2010-07-06T00:00:00Z
review text: A word \(v\in A^*\) is an internal factor of a word \(x\in A^*\) iff \(x=uvw\) for some nonempty words \(u,w\). The kernel of a set \(X\subset A^*\) is the set of words from \(X\) which are internal factors of some word from \(X\). It is shown, that if \(X\) is a code with empty kernel, \(F\) the set of internal factors of words from \(X\) and \(\varphi\) the syntactic morphism of the submonoid \(X^*\), then any group \(G\) contained in \(\varphi(A^*\setminus F)\) is cyclic. A subclass of codes with empty kernel are semaphore codes, thus this is a generalization of a result of \textit{M. P. Schützenberger} [Inf. Control 7, 23-26 (1964; Zbl 0122.15004)].
reviewed by: Jaak Henno
Mathematics Subject Classification ID: 20M35
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 68Q45
zbMATH DE Number: 5730956
zbMATH Keywords: codes
zbMATH Keywords: kernels of sets of words
zbMATH Keywords: syntactic semigroups
zbMATH Keywords: finite automata
zbMATH Keywords: internal factors
MaRDI profile type: Publication
full work available at URL: s00233-010-9214-5
OpenAlex ID: W1975783797
cites work: Q3653240
cites work: Algorithms for computing finite semigroups
cites work: Q3853827
cites work: On the synchronizing properties of certain prefix codes
cites work: Q4046274
cites work: Q5512231
DOI: 10.1007/S00233-010-9214-5
description: scientific article; zbMATH DE number 5730956