Commutator theory for racks and quandles
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10436396" target="_blank" >RIV/00216208:11320/21:10436396 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=T7cU82kQbl" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=T7cU82kQbl</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2969/jmsj/83168316" target="_blank" >10.2969/jmsj/83168316</a>
Alternative languages
Result language
angličtina
Original language name
Commutator theory for racks and quandles
Original language description
We adapt the commutator theory of universal algebra to the particular setting of racks and quandles, exploiting a Galois connection between congruences and certain normal subgroups of the displacement group. Congruence properties, such as abelianness and centrality, are reflected by the corresponding relative displacement groups, and the global properties, solvability and nilpotence, are reflected by the properties of the whole displacement group. To show the new tool in action, we present three applications: nonexistence theorems for quandles (no connected involutory quandles of order 2(k), no latin quandles of order equivalent to 2 (mod 4)), a non-colorability theorem (knots with trivial Alexander polynomial are not colorable by solvable quandles; in particular, by finite latin quandles), and a strengthening of Glauberman's results on Bruck loops of odd order.
Czech name
—
Czech description
—
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/GA18-20123S" target="_blank" >GA18-20123S: Expanding the Scope of Universal Algebra</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of the Mathematical Society of Japan
ISSN
0025-5645
e-ISSN
—
Volume of the periodical
2021
Issue of the periodical within the volume
73
Country of publishing house
JP - JAPAN
Number of pages
35
Pages from-to
41-75
UT code for WoS article
000612519000002
EID of the result in the Scopus database
2-s2.0-85101004276