Rescuing the Whitehead method for free products. II: The algorithm
type: Item
instance of: scholarly article
title: Rescuing the Whitehead method for free products. II: The algorithm
zbMATH Open document ID: 0542.20012
DOI: 10.1007/BF01174888
author: Donald J. Collins
author: Heiner Zieschang
published in: Mathematische Zeitschrift
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173450
review text: The authors continue their study of adapting the Whitehead method on the free products of groups begun in a previous paper [Part I, ibid. 185, 487-504 (1984; Zbl 0537.20010)]. In the present paper they use their theorem to describe, under some assumptions on the factors and some additional argument, an algorithm to decide whether two elements of the free product belong to the same automorphism class. They again consider free products of finitely many (freely) indecomposable factors and distinguish two cases, the first being the case where none of the factors is infinite cyclic and the second the general case. Finally they give some examples and applications of their method.
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20F10
zbMATH DE Number: 3861420
zbMATH Keywords: Whitehead automorphism
zbMATH Keywords: algorithm
zbMATH Keywords: automorphism class
zbMATH Keywords: free products
zbMATH Keywords: indecomposable factors
MaRDI profile type: Publication
cites work: Rescuing the Whitehead method for free products. I: Peak reduction
cites work: Some general algorithms. II: Nilpotent groups
cites work: On Certain Sets of Elements in a Free Group
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cites work: Über Worte \(S_1^{a_1}, S_2^{a_2}, \ldots, S_q^{a_q}\) in einer freien Gruppe mit \(p\) freien Erzeugenden
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description: scientific article; zbMATH DE number 3861420