An extension formula for right Bol loops arising from Bol reflections

We study a new extension formula for right Bol loops. We prove the necessary or sufficient conditions for the extension to be right Bol. We describe the most important invariants: right multiplication group, nuclei, and center. We show that the core is an involutory quandle which is the disjoint uni...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Communications in algebra Ročník 52; číslo 12; s. 5150 - 5164
Hlavní autoři: Galici, Mario, Nagy, Gábor P.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 01.12.2024
Taylor & Francis Ltd
Témata:
Loops
nets
ISSN:0092-7872, 1532-4125
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Abstract We study a new extension formula for right Bol loops. We prove the necessary or sufficient conditions for the extension to be right Bol. We describe the most important invariants: right multiplication group, nuclei, and center. We show that the core is an involutory quandle which is the disjoint union of two isomorphic involutory quandles. We also derive further results on the structure group of the core of the extension.
AbstractList We study a new extension formula for right Bol loops. We prove the necessary or sufficient conditions for the extension to be right Bol. We describe the most important invariants: right multiplication group, nuclei, and center. We show that the core is an involutory quandle which is the disjoint union of two isomorphic involutory quandles. We also derive further results on the structure group of the core of the extension.
Author Galici, Mario
Nagy, Gábor P.
Author_xml – sequence: 1
  givenname: Mario
  surname: Galici
  fullname: Galici, Mario
  organization: Dipartimento di Matematica e Informatica, UniversitÀ degli Studi di Palermo
– sequence: 2
  givenname: Gábor P.
  surname: Nagy
  fullname: Nagy, Gábor P.
  organization: HUN-REN-ELTE Geometric and Algebraic Combinatorics Research Group
BookMark eNqFkE1LAzEURYNUsK3-BGHA9dR8TJIZ3FhL_YCCG12HdCapKWlSkxTtv3di68aFrh6Ee17uOyMwcN4pAC4RnCBYw2sIG8xrjicY4mqCCeOIoRMwRJTgskKYDsAwZ8ocOgOjGNcQIsprPATzqSvUZ1IuGu8K7cNmZ2WeRTCrt1TceVtY77exkMFE41aFDn7z_RyUtqpNPRfPwamWNqqL4xyD1_v5y-yxXDw_PM2mi7IlpE5lo5TSiLeVpHzZVA3HGncat5jwZY0kg5zSji0RI4o1UjKuJYWK666qCSdIkjG4OuzdBv--UzGJtd8F138pCOoPZxWDrE_dHFJt8DH2NUVrksxFU5DGCgRF9iZ-vInsTRy99TT9RW-D2ciw_5e7PXDGZY3ywwfbiST31gcdpGtNLvnnii8PG4V_
CitedBy_id crossref_primary_10_1002_jcd_21964
Cites_doi 10.1007/b83276
10.1016/j.disc
10.1016/j.jalgebra.2005.03.005
10.1017/S0305004106009625
10.1016/j.jpaa.2015.07.014
10.1090/S0002-9947-07-04391-7
10.1007/978-3-642-65616-3
10.1007/BF01226801
10.5486/PMD.1968.15.1-4.27
10.1016/0001-8708(83)90013-0
10.5486/PMD.1969.16.1-4.26
10.1016/j.jpaa.2020.106474
10.1016/0021-8693(86)90075-X
10.2307/1996765
10.1090/S0002-9947-09-04646-7
10.4153/CJM-1994-059-8
10.1515/9783110900583
10.1017/S030500419900403X
ContentType Journal Article
Copyright 2024 Taylor & Francis Group, LLC 2024
2024 Taylor & Francis Group, LLC
Copyright_xml – notice: 2024 Taylor & Francis Group, LLC 2024
– notice: 2024 Taylor & Francis Group, LLC
DBID AAYXX
CITATION
7SC
8FD
JQ2
L7M
L~C
L~D
DOI 10.1080/00927872.2024.2367161
DatabaseName CrossRef
Computer and Information Systems Abstracts
Technology Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Computer and Information Systems Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Advanced Technologies Database with Aerospace
ProQuest Computer Science Collection
Computer and Information Systems Abstracts Professional
DatabaseTitleList Computer and Information Systems Abstracts
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1532-4125
EndPage 5164
ExternalDocumentID 10_1080_00927872_2024_2367161
2367161
Genre Research Article
GrantInformation_xml – fundername: NKFIH-OTKA
  grantid: SNN 132625
– fundername: Ministry of Innovation and Technology of Hungary
– fundername: National Research, Development and Innovation Fund
  grantid: TKP2021-NVA
GroupedDBID -DZ
-~X
.7F
.QJ
0BK
0R~
29F
2DF
30N
4.4
5GY
5VS
AAENE
AAGDL
AAHIA
AAJMT
AALDU
AAMIU
AAPUL
AAQRR
ABCCY
ABFIM
ABHAV
ABJNI
ABLIJ
ABPAQ
ABPEM
ABTAI
ABXUL
ABXYU
ACGEJ
ACGFS
ACTIO
ADCVX
ADGTB
ADXPE
AEISY
AENEX
AEOZL
AEPSL
AEYOC
AFKVX
AFRVT
AGDLA
AGMYJ
AHDZW
AIJEM
AIYEW
AJWEG
AKBVH
AKOOK
ALMA_UNASSIGNED_HOLDINGS
ALQZU
AQRUH
AQTUD
AVBZW
AWYRJ
BLEHA
CCCUG
CE4
CS3
DGEBU
DKSSO
DU5
EBS
E~A
E~B
GTTXZ
H13
HF~
HZ~
H~P
IPNFZ
J.P
KYCEM
LJTGL
M4Z
NA5
NY~
O9-
P2P
PQQKQ
RIG
RNANH
ROSJB
RTWRZ
S-T
SNACF
TASJS
TBQAZ
TDBHL
TEJ
TFL
TFT
TFW
TN5
TOXWX
TTHFI
TUROJ
TWF
UPT
UT5
UU3
WH7
XSW
ZGOLN
~S~
07G
1TA
6TJ
AAGZG
AAIKQ
AAKBW
AAYXX
ACAGQ
ACGEE
ACTCW
AEUMN
AGCQS
AGLEN
AGROQ
AHMOU
ALCKM
AMEWO
AMVHM
AMXXU
BCCOT
BPLKW
C06
CAG
CITATION
COF
CRFIH
DMQIW
DWIFK
EJD
H~9
IVXBP
MVM
NUSFT
OHT
QCRFL
TAQ
TFMCV
UB9
UU8
V3K
V4Q
ZY4
7SC
8FD
ADYSH
JQ2
L7M
L~C
L~D
ID FETCH-LOGICAL-c338t-9eeef17c4a57b94972f2df2c237b81a60755d6b163e69aa67fa50e7fd483731a3
IEDL.DBID TFW
ISICitedReferencesCount 1
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001270083200001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0092-7872
IngestDate Sat Jul 26 00:21:32 EDT 2025
Sat Nov 29 02:27:54 EST 2025
Tue Nov 18 21:01:40 EST 2025
Mon Oct 20 23:45:41 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 12
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c338t-9eeef17c4a57b94972f2df2c237b81a60755d6b163e69aa67fa50e7fd483731a3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
PQID 3123664606
PQPubID 2045307
PageCount 15
ParticipantIDs crossref_citationtrail_10_1080_00927872_2024_2367161
proquest_journals_3123664606
crossref_primary_10_1080_00927872_2024_2367161
informaworld_taylorfrancis_310_1080_00927872_2024_2367161
PublicationCentury 2000
PublicationDate 2024-12-01
PublicationDateYYYYMMDD 2024-12-01
PublicationDate_xml – month: 12
  year: 2024
  text: 2024-12-01
  day: 01
PublicationDecade 2020
PublicationPlace Abingdon
PublicationPlace_xml – name: Abingdon
PublicationTitle Communications in algebra
PublicationYear 2024
Publisher Taylor & Francis
Taylor & Francis Ltd
Publisher_xml – name: Taylor & Francis
– name: Taylor & Francis Ltd
References e_1_3_2_27_1
e_1_3_2_20_1
Nagy G. (e_1_3_2_19_1) 1994; 14
e_1_3_2_21_1
e_1_3_2_22_1
e_1_3_2_23_1
e_1_3_2_24_1
e_1_3_2_26_1
e_1_3_2_16_1
e_1_3_2_9_1
e_1_3_2_8_1
e_1_3_2_18_1
e_1_3_2_7_1
e_1_3_2_2_1
e_1_3_2_10_1
e_1_3_2_11_1
e_1_3_2_6_1
e_1_3_2_12_1
e_1_3_2_5_1
e_1_3_2_13_1
e_1_3_2_14_1
e_1_3_2_3_1
e_1_3_2_15_1
Belousov V. D. (e_1_3_2_4_1) 1967
Pflugfelder H. O. (e_1_3_2_25_1) 1990
Loos O. (e_1_3_2_17_1) 1969
References_xml – ident: e_1_3_2_14_1
  doi: 10.1007/b83276
– start-page: 176
  volume-title: Foundations of the Theory of Quasigroups and Loops
  year: 1967
  ident: e_1_3_2_4_1
– ident: e_1_3_2_21_1
  doi: 10.1016/j.disc
– ident: e_1_3_2_2_1
  doi: 10.1016/j.jalgebra.2005.03.005
– ident: e_1_3_2_20_1
  doi: 10.1017/S0305004106009625
– ident: e_1_3_2_13_1
  doi: 10.1016/j.jpaa.2015.07.014
– ident: e_1_3_2_15_1
  doi: 10.1090/S0002-9947-07-04391-7
– volume-title: Quasigroups and Loops: Introduction
  year: 1990
  ident: e_1_3_2_25_1
– ident: e_1_3_2_26_1
  doi: 10.1007/978-3-642-65616-3
– ident: e_1_3_2_8_1
  doi: 10.1007/BF01226801
– ident: e_1_3_2_27_1
– ident: e_1_3_2_6_1
  doi: 10.5486/PMD.1968.15.1-4.27
– volume: 14
  start-page: 115
  issue: 1
  year: 1994
  ident: e_1_3_2_19_1
  article-title: Collineation groups of the smallest Bol 3-nets
  publication-title: Note Mat
– ident: e_1_3_2_3_1
  doi: 10.1016/0001-8708(83)90013-0
– ident: e_1_3_2_18_1
– ident: e_1_3_2_7_1
  doi: 10.5486/PMD.1969.16.1-4.26
– volume-title: Symmetric Spaces: General Theory
  year: 1969
  ident: e_1_3_2_17_1
– ident: e_1_3_2_9_1
– ident: e_1_3_2_16_1
  doi: 10.1016/j.jpaa.2020.106474
– ident: e_1_3_2_10_1
  doi: 10.1016/0021-8693(86)90075-X
– ident: e_1_3_2_5_1
  doi: 10.2307/1996765
– ident: e_1_3_2_11_1
– ident: e_1_3_2_22_1
  doi: 10.1090/S0002-9947-09-04646-7
– ident: e_1_3_2_23_1
  doi: 10.4153/CJM-1994-059-8
– ident: e_1_3_2_24_1
  doi: 10.1515/9783110900583
– ident: e_1_3_2_12_1
  doi: 10.1017/S030500419900403X
SSID ssj0015782
Score 2.3756874
Snippet We study a new extension formula for right Bol loops. We prove the necessary or sufficient conditions for the extension to be right Bol. We describe the most...
SourceID proquest
crossref
informaworld
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 5150
SubjectTerms Loops
nets
Title An extension formula for right Bol loops arising from Bol reflections
URI https://www.tandfonline.com/doi/abs/10.1080/00927872.2024.2367161
https://www.proquest.com/docview/3123664606
Volume 52
WOSCitedRecordID wos001270083200001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAWR
  databaseName: Taylor & Francis Journals Complete
  customDbUrl:
  eissn: 1532-4125
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0015782
  issn: 0092-7872
  databaseCode: TFW
  dateStart: 19740101
  isFulltext: true
  titleUrlDefault: https://www.tandfonline.com
  providerName: Taylor & Francis
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07T8MwELZQxQADb0ShIA-sKY3t2PVYUCsWKoYiukV2YktIUVI1Kb8fn_MQFUIdYIqS6CznfPY9cvcdQveWh6lhaRRwQkTApJWBYmIUSKUFJalyGl_7ZhNiPh8vl_K1ySYsm7RK8KFtDRThz2rY3EqXbUbcA-AEOTmDMirChgBBFnoHyKl-2JqL2Xv3HwHA2mscSmdHOpK2hue3Uba00xZ26Y-z2iug2fE_TP0EHTXWJ57U4nKK9kx-hg5fOujW8hxNJzn2kXEIo2GY2SZTcMXej8ePRYazoliVGNoXOsWHoULFP3afk_nMrry8QG-z6eLpOWh6LQSJc1KrQBpjbCgSpiKhJZOCWJJakhAq9DhU3FkWUcq1s94Ml0pxYVU0MsKmgEhPQ0UvUS8vcnOFsDNQKCUjrZVJoR5Lacq1kFKNNbPc0D5iLY_jpAEih34YWRx2eKU1l2LgUtxwqY-GHdmqRuLYRSC_L2Bc-RCIrfuVxHQH7aBd7bjZ1EDi3nLmXL7rPwx9gw7gtk6JGaBetd6YW7SffFYf5frOi-8XNJDo1w
linkProvider Taylor & Francis
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3NS8MwFA-ignrwW5xOzcFr55qkyXKcsjFx22nibiVpExBKO_bh329e2o0NkR30VGh4IX15yfvoe7-H0KPlYWpYGgWcEBEwaWWgmGgGUmlBSaqcxte-2YQYDlvjsVyvhYG0SvChbQkU4e9qONwQjF6mxD0BUJATNKijIqwBGGQheEB7kdO1gJ8_6n6s_iQAXHuJROksSUezrOL5bZoN_bSBXvrjtvYqqHvyH4s_RceVAYrbpcScoR2Tn6OjwQq9dXaBOu0c--A4RNIwLG2RKXhi78rj5yLDWVFMZhg6GDrdh6FIxb9235P55K58doneu53RSy-o2i0EifNT54E0xthQJExFQksmBbEktSQhVOhWqLgzLqKUa2fAGS6V4sKqqGmETQGUnoaKXqHdvMjNNcLORqGUNLVWJoWSLKUp10JK1dLMckNriC2ZHCcVFjm0xMjicAVZWnIpBi7FFZdqqLEim5RgHNsI5PoOxnMfBbFly5KYbqGtL7c7rs41kLhRzpzXd_OHqR_QQW806Mf91-HbLTqEoTJDpo5259OFuUP7ydf8cza997L8DQo27QE
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3NS8MwFA8yRfTgtzidmoPXzjXJkuU4dUNRxw4TdytJm4BQurF2_v3mpd1wiOygp0LDC-nLS95H3_s9hG4sDxPDknbACREBk1YGiolWIJUWlCTKaXztm02IwaAzHsthlU2YV2mV4EPbEijC39VwuKeJXWTE3QJOkJMzKKMirAkQZCE4QJvOdOYg5KP--_JHAqC1l0CUzpB0NIsint-mWVFPK-ClPy5rr4H6-_-w9gO0V5mfuFvKyyHaMNkR2n1dYrfmx6jXzbAPjUMcDcPK5qmCJ_aOPL6bpDidTKY5hv6FTvNhKFHxr93npD61K8tP0Fu_N7p_DKpmC0HsvNQikMYYG4qYqbbQkklBLEksiQkVuhMq7kyLdsK1M98Ml0pxYVW7ZYRNAJKehoqeolo2ycwZws5CoZS0tFYmgYIspSnXQkrV0cxyQ-uILXgcxRUSOTTESKNwCVhacikCLkUVl-qouSSbllAc6wjk9w2MCh8DsWXDkoiuoW0sdjuqTjWQuFHOnM93_oepr9H28KEfvTwNni_QDoyU6TENVCtmc3OJtuLP4iOfXXlJ_gJCGuuz
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=An+extension+formula+for+right+Bol+loops+arising+from+Bol+reflections&rft.jtitle=Communications+in+algebra&rft.au=Galici%2C+Mario&rft.au=Nagy%2C+G%C3%A1bor+P.&rft.date=2024-12-01&rft.issn=0092-7872&rft.eissn=1532-4125&rft.volume=52&rft.issue=12&rft.spage=5150&rft.epage=5164&rft_id=info:doi/10.1080%2F00927872.2024.2367161&rft.externalDBID=n%2Fa&rft.externalDocID=10_1080_00927872_2024_2367161
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0092-7872&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0092-7872&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0092-7872&client=summon