Construction d'une famille de codes associés à certains groupes finis. (Construction of a family of codes associated to certain finite groups)
type: Item
instance of: scholarly article
title: Construction d'une famille de codes associés à certains groupes finis. (Construction of a family of codes associated to certain finite groups)
zbMATH Open document ID: 0668.20070
DOI: 10.1016/0304-3975(87)90127-7
author: Giuseppina Rindone
published in: Theoretical Computer Science
publication date: 1987-01-01T00:00:00Z
review text: The author shows the optimality of the Perrin conjecture extending Schreier's formula for subgroups of free groups to free monoids. A code on an alphabet A is a subset X of \(A^*\) freely generating \(X^*\). Suppose Q is a set, \(q\in Q\), G is a group acting on Q and H is the subgroup of G fixing q. For any surjective homomorphism f: \(A^*\to G\), \(f^{-1}(H)\) is free and the generating code will be denoted by \(Z<G,H,f>\). Theorem 1: Let G be a noncyclic group of degree d and let X be a finite subset of \(Z<G,H,f>\). If G is a syntactic group of \(X^*\), then X has at least \(d+1\) elements. Theorem 2: Let G be an abelian group of rank 2 and degree d. Then there is a code X on \(\{\) a,b\(\}\) of \(d+1\) elements so that G is a syntactic group of \(X^*\).
Mathematics Subject Classification ID: 20M35
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 68Q70
zbMATH DE Number: 4093791
zbMATH Keywords: Perrin conjecture
zbMATH Keywords: subgroups of free groups
zbMATH Keywords: free monoids
zbMATH Keywords: code
zbMATH Keywords: alphabet
zbMATH Keywords: generating code
zbMATH Keywords: syntactic group
reviewed by: Awad A. Iskander
MaRDI profile type: Publication
full work available at URL: 0304-3975(87)90127-7
OpenAlex ID: W1966636504
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description: scientific article; zbMATH DE number 4093791