On isotopes of groups. II
We select canonical decompositions of the isotopes of groups, show that they are unique, and establish relationships between them. We also obtain external characteristics of the identities which imply the linearity or alinearity of the isotopy and the commutativity of the corresponding group. We des...
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| Date: | 1995 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1995
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5563 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511797112471552 |
|---|---|
| author | Sokhats’kyi, F. M. Сохацький, Ф. М. |
| author_facet | Sokhats’kyi, F. M. Сохацький, Ф. М. |
| author_sort | Sokhats’kyi, F. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:13:33Z |
| description | We select canonical decompositions of the isotopes of groups, show that they are unique, and establish relationships between them. We also obtain external characteristics of the identities which imply the linearity or alinearity of the isotopy and the commutativity of the corresponding group. We describe the identities of linear isotopes of Abelian groups, i.e., ofT-quasigroups, and suggest a new method for the description of isotopic closures of classes of groups. |
| first_indexed | 2026-03-24T03:18:36Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5563 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:18:36Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b2/91261f473c101df7f3199c1b2b1fdbb2.pdf |
| spelling | umjimathkievua-article-55632020-03-19T09:13:33Z On isotopes of groups. II Про ізотопи груп. II Sokhats’kyi, F. M. Сохацький, Ф. М. We select canonical decompositions of the isotopes of groups, show that they are unique, and establish relationships between them. We also obtain external characteristics of the identities which imply the linearity or alinearity of the isotopy and the commutativity of the corresponding group. We describe the identities of linear isotopes of Abelian groups, i.e., ofT-quasigroups, and suggest a new method for the description of isotopic closures of classes of groups. Виділено канонічні розклади ізотопів груп, встанбвлено їх однозначність і знайдено співвідношення між ними. Встановлено зовнішні характеристики тотожностей, виконання яких дає лінійність чи алінійність ізотопії і комутативність відповідної групи. Описано тотожності лінійних ізотопів абелевих груп, тобто $T$-квазігруп. Дано новий метод опису ізотопних замикань класів груп. Institute of Mathematics, NAS of Ukraine 1995-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5563 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 12 (1995); 1692–1703 Український математичний журнал; Том 47 № 12 (1995); 1692–1703 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5563/7814 https://umj.imath.kiev.ua/index.php/umj/article/view/5563/7815 Copyright (c) 1995 Sokhats’kyi F. M. |
| spellingShingle | Sokhats’kyi, F. M. Сохацький, Ф. М. On isotopes of groups. II |
| title | On isotopes of groups. II |
| title_alt | Про ізотопи груп. II |
| title_full | On isotopes of groups. II |
| title_fullStr | On isotopes of groups. II |
| title_full_unstemmed | On isotopes of groups. II |
| title_short | On isotopes of groups. II |
| title_sort | on isotopes of groups. ii |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5563 |
| work_keys_str_mv | AT sokhatskyifm onisotopesofgroupsii AT sohacʹkijfm onisotopesofgroupsii AT sokhatskyifm proízotopigrupii AT sohacʹkijfm proízotopigrupii |