Every Finite Nilpotent Loop has a Supernilpotent Loop as Reduct
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509157" target="_blank" >RIV/00216208:11320/25:10509157 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=_ubct89b_D" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=_ubct89b_D</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00025-025-02568-2" target="_blank" >10.1007/s00025-025-02568-2</a>
Alternative languages
Result language
angličtina
Original language name
Every Finite Nilpotent Loop has a Supernilpotent Loop as Reduct
Original language description
A basic fact taught in undergraduate algebra courses is that every finite nilpotent group is a direct product of p-groups. Already Bruck [5] observed that this does not generalize to loops. In particular, there exist nilpotent loops of size 6 which are not direct products of loops of size 2 and 3. Still we show that every finite nilpotent loop (A,<middle dot>)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$(A,cdot )$$end{document} has a binary term operation & lowast;documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$*$$end{document} such that (A,& lowast;)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$(A,*)$$end{document} is a direct product of nilpotent loops of prime power order, i.e., (A,& lowast;)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$(A,*)$$end{document} is supernilpotent. As an application we obtain that every nilpotent loop of order pq for primes p, q has a finite basis for its equational theory.
Czech name
—
Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA25-16324S" target="_blank" >GA25-16324S: Characterization and tractability of constraint languages via logical methods</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Results in Mathematics
ISSN
1422-6383
e-ISSN
1420-9012
Volume of the periodical
81
Issue of the periodical within the volume
1
Country of publishing house
CH - SWITZERLAND
Number of pages
16
Pages from-to
21
UT code for WoS article
001643176700001
EID of the result in the Scopus database
2-s2.0-105025261656