On embedding groups into digroups

Yurii Zhuchok; Günter Pilz; Anatolii V. Zhuchok

doi:10.12958/adm2364

On embedding groups into digroups

Yurii Zhuchok
, Günter Pilz
, Anatolii V. Zhuchok

Institute for Algebra

Research output: Contribution to journal › Article › peer-review

Abstract

We show that any group (semigroup) can be embedded into a suitable non-trivial digroup (dimonoid).We present a universal extension for an arbitrary dimonoid, givea construction of the free abelian generalized digroup and characterize the least group congruence on it.

Original language	English
Pages (from-to)	270-287
Number of pages	18
Journal	Algebra and Discrete Mathematics
Volume	38
Issue number	2
DOIs	https://doi.org/10.12958/adm2364
Publication status	Published - 2024

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101013 Mathematical logic
102031 Theoretical computer science

JKU Focus areas

Digital Transformation

Access to Document

10.12958/adm2364

Cite this

@article{2b02506e3b654458890e728b33e28768,

title = "On embedding groups into digroups",

abstract = "We show that any group (semigroup) can be embedded into a suitable non-trivial digroup (dimonoid).We present a universal extension for an arbitrary dimonoid, givea construction of the free abelian generalized digroup and characterize the least group congruence on it.",

author = "Yurii Zhuchok and G{\"u}nter Pilz and Zhuchok, \{Anatolii V.\}",

year = "2024",

doi = "10.12958/adm2364",

language = "English",

volume = "38",

pages = "270--287",

journal = "Algebra and Discrete Mathematics",

issn = "1726-3255",

publisher = "Elsevier",

number = "2",

}

TY - JOUR

T1 - On embedding groups into digroups

AU - Zhuchok, Yurii

AU - Pilz, Günter

AU - Zhuchok, Anatolii V.

PY - 2024

Y1 - 2024

N2 - We show that any group (semigroup) can be embedded into a suitable non-trivial digroup (dimonoid).We present a universal extension for an arbitrary dimonoid, givea construction of the free abelian generalized digroup and characterize the least group congruence on it.

AB - We show that any group (semigroup) can be embedded into a suitable non-trivial digroup (dimonoid).We present a universal extension for an arbitrary dimonoid, givea construction of the free abelian generalized digroup and characterize the least group congruence on it.

UR - https://www.scopus.com/pages/publications/85216787326

U2 - 10.12958/adm2364

DO - 10.12958/adm2364

M3 - Article

SN - 1726-3255

VL - 38

SP - 270

EP - 287

JO - Algebra and Discrete Mathematics

JF - Algebra and Discrete Mathematics

IS - 2

ER -

On embedding groups into digroups

Abstract

Fields of science

JKU Focus areas

Access to Document

Other files and links

Cite this