On the Root-Class Residuallity of Generalized Free Products

On the Root-Class Residuallity of Generalized Free Products

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Let K be a root class of groups. It is proved that a free product of any family of residually K groups with one amalgamated subgroup, which is a retract in all free factors, is residually K. The sufficient condition for a generalized free product of two groups to be residually K is also obtained, pr...

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Bibliographic Details
Main Author: E. A. Tumanova
Format: Article
Language:English
Published: Yaroslavl State University 2013-02-01
Series:Modelirovanie i Analiz Informacionnyh Sistem
Subjects:
free product with one amalgamated subgroup
root class of groups
root-class residuallity
retract
Online Access:https://www.mais-journal.ru/jour/article/view/225
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spelling doaj-60a755751db34d8990982a27cabb1b502021-07-29T08:15:18ZengYaroslavl State UniversityModelirovanie i Analiz Informacionnyh Sistem1818-10152313-54172013-02-0120113313710.18255/1818-1015-2013-1-133-137218On the Root-Class Residuallity of Generalized Free ProductsE. A. Tumanova0Ivanovo State UniversityLet K be a root class of groups. It is proved that a free product of any family of residually K groups with one amalgamated subgroup, which is a retract in all free factors, is residually K. The sufficient condition for a generalized free product of two groups to be residually K is also obtained, provided that the amalgamated subgroup is normal in one of the free factors and is a retract in another.https://www.mais-journal.ru/jour/article/view/225free product with one amalgamated subgrouproot class of groupsroot-class residuallityretract
collection DOAJ
language English
format Article
sources DOAJ
author E. A. Tumanova
spellingShingle E. A. Tumanova
On the Root-Class Residuallity of Generalized Free Products
Modelirovanie i Analiz Informacionnyh Sistem
free product with one amalgamated subgroup
root class of groups
root-class residuallity
retract
author_facet E. A. Tumanova
author_sort E. A. Tumanova
title On the Root-Class Residuallity of Generalized Free Products
title_short On the Root-Class Residuallity of Generalized Free Products
title_full On the Root-Class Residuallity of Generalized Free Products
title_fullStr On the Root-Class Residuallity of Generalized Free Products
title_full_unstemmed On the Root-Class Residuallity of Generalized Free Products
title_sort on the root-class residuallity of generalized free products
publisher Yaroslavl State University
series Modelirovanie i Analiz Informacionnyh Sistem
issn 1818-1015
2313-5417
publishDate 2013-02-01
description Let K be a root class of groups. It is proved that a free product of any family of residually K groups with one amalgamated subgroup, which is a retract in all free factors, is residually K. The sufficient condition for a generalized free product of two groups to be residually K is also obtained, provided that the amalgamated subgroup is normal in one of the free factors and is a retract in another.
topic free product with one amalgamated subgroup
root class of groups
root-class residuallity
retract
url https://www.mais-journal.ru/jour/article/view/225
work_keys_str_mv AT eatumanova ontherootclassresiduallityofgeneralizedfreeproducts
_version_ 1721256569009602560

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