On embedding groups into digroups
An idea of the notion of a digroup which generalizes groups and has close relationships with the dimonoids, trioids, Leibniz algebras and other structures was proposed by J.-L. Loday. In terms of digroups, Kinyon obtained an analogue of Lie’s third theorem for the class of so-called split Leibniz al...
Збережено в:
| Дата: | 2025 |
|---|---|
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2025
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2364 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| id |
oai:ojs.admjournal.luguniv.edu.ua:article-2364 |
|---|---|
| record_format |
ojs |
| spelling |
oai:ojs.admjournal.luguniv.edu.ua:article-23642025-01-19T19:44:59Z On embedding groups into digroups Zhuchok, Yurii V. Pilz, Guenter F. Zhuchok, Anatolii V. semigroup, group, dimonoid, digroup, congruence An idea of the notion of a digroup which generalizes groups and has close relationships with the dimonoids, trioids, Leibniz algebras and other structures was proposed by J.-L. Loday. In terms of digroups, Kinyon obtained an analogue of Lie’s third theorem for the class of so-called split Leibniz algebras. In this paper, we use group operations (semigroup operations) to construct new digroups (dimonoids) and show that any group (semigroup) can be embedded into a suitable non-trivial digroup (dimonoid). We present a universal extension for an arbitrary dimonoid, give a construction of the free abelian generalized digroup and characterize the least group congruence on it. We also describe the least abelian digroup congruence on the free generalized digroup. Lugansk National Taras Shevchenko University 2025-01-19 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2364 10.12958/adm2364 Algebra and Discrete Mathematics; Vol 38, No 2 (2024): A special issue 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2364/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2364/1282 Copyright (c) 2025 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2025-01-19T19:44:59Z |
| collection |
OJS |
| language |
English |
| topic |
semigroup group dimonoid digroup congruence |
| spellingShingle |
semigroup group dimonoid digroup congruence Zhuchok, Yurii V. Pilz, Guenter F. Zhuchok, Anatolii V. On embedding groups into digroups |
| topic_facet |
semigroup group dimonoid digroup congruence |
| format |
Article |
| author |
Zhuchok, Yurii V. Pilz, Guenter F. Zhuchok, Anatolii V. |
| author_facet |
Zhuchok, Yurii V. Pilz, Guenter F. Zhuchok, Anatolii V. |
| author_sort |
Zhuchok, Yurii V. |
| title |
On embedding groups into digroups |
| title_short |
On embedding groups into digroups |
| title_full |
On embedding groups into digroups |
| title_fullStr |
On embedding groups into digroups |
| title_full_unstemmed |
On embedding groups into digroups |
| title_sort |
on embedding groups into digroups |
| description |
An idea of the notion of a digroup which generalizes groups and has close relationships with the dimonoids, trioids, Leibniz algebras and other structures was proposed by J.-L. Loday. In terms of digroups, Kinyon obtained an analogue of Lie’s third theorem for the class of so-called split Leibniz algebras. In this paper, we use group operations (semigroup operations) to construct new digroups (dimonoids) and show that any group (semigroup) can be embedded into a suitable non-trivial digroup (dimonoid). We present a universal extension for an arbitrary dimonoid, give a construction of the free abelian generalized digroup and characterize the least group congruence on it. We also describe the least abelian digroup congruence on the free generalized digroup. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2025 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2364 |
| work_keys_str_mv |
AT zhuchokyuriiv onembeddinggroupsintodigroups AT pilzguenterf onembeddinggroupsintodigroups AT zhuchokanatoliiv onembeddinggroupsintodigroups |
| first_indexed |
2025-01-08T04:02:55Z |
| last_indexed |
2025-01-20T04:04:24Z |
| _version_ |
1827356167300448256 |