On the Root-Class Residuallity of Generalized Free Products
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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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2013-02-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/225 |
| _version_ | 1797877947825127424 |
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| author | E. A. Tumanova |
| author_facet | E. A. Tumanova |
| author_sort | E. A. Tumanova |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-10T02:24:51Z |
| format | Article |
| id | doaj.art-60a755751db34d8990982a27cabb1b50 |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2024-04-10T02:24:51Z |
| publishDate | 2013-02-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-60a755751db34d8990982a27cabb1b502023-03-13T08:07:31ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172013-02-0120113313710.18255/1818-1015-2013-1-133-137218On the Root-Class Residuallity of Generalized Free ProductsE. A. Tumanova0Ивановский государственный университетLet 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/225свободное произведение с одной объединенной подгруппойкорневой класс группаппроксимируемость корневыми классами группретракт |
| spellingShingle | E. A. Tumanova On the Root-Class Residuallity of Generalized Free Products Моделирование и анализ информационных систем свободное произведение с одной объединенной подгруппой корневой класс групп аппроксимируемость корневыми классами групп ретракт |
| title | 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_short | On the Root-Class Residuallity of Generalized Free Products |
| title_sort | on the root class residuallity of generalized free products |
| topic | свободное произведение с одной объединенной подгруппой корневой класс групп аппроксимируемость корневыми классами групп ретракт |
| url | https://www.mais-journal.ru/jour/article/view/225 |
| work_keys_str_mv | AT eatumanova ontherootclassresiduallityofgeneralizedfreeproducts |