Middle Bruck Loops and the Total Multiplication Group
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10452394" target="_blank" >RIV/00216208:11320/22:10452394 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=XKLBsNFunr" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=XKLBsNFunr</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00025-022-01716-2" target="_blank" >10.1007/s00025-022-01716-2</a>
Alternative languages
Result language
angličtina
Original language name
Middle Bruck Loops and the Total Multiplication Group
Original language description
Let Q be a loop. The mappings x bar right arrow ax, x bar right arrow xa and x bar right arrow a/x are denoted by L-a, R-a. and D-a, respectively. The loop is said to be middle Bruck if for all a, b is an element of Q there exists c is an element of Q such that DaDbDa = D-c. The right inverse of Q is the loop with operation x/(y1). It is proved that Q is middle Bruck if and only if the right inverse of Q is left Bruck (i.e., a left Bol loop in which (xy)(-1) = x(-1) y(-1)). Middle Bruck loops are characterized in group theoretic language as transversals T to H <= G such that < T > = G, T-G = T and t(2) = 1 for each t is an element of T. Other results include the fact that if Q is a finite loop, then the total multiplication group < L-a, R-a, D-a; a is an element of Q > is nilpotent if and only if Q is a centrally nilpotent 2-loop, and the fact that total multiplication groups of paratopic loops are isomorphic.
Czech name
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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
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
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
77
Issue of the periodical within the volume
4
Country of publishing house
CH - SWITZERLAND
Number of pages
27
Pages from-to
174
UT code for WoS article
000824640300001
EID of the result in the Scopus database
2-s2.0-85134315033