A short proof for the central nilpotency of Moufang loops of prime power order

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10471878" target="_blank" >RIV/00216208:11320/23:10471878 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=dJZBxtGlJr" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=dJZBxtGlJr</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jalgebra.2023.07.025" target="_blank" >10.1016/j.jalgebra.2023.07.025</a>

Result language
angličtina
Original language name
A short proof for the central nilpotency of Moufang loops of prime power order
Original language description
The main result is an elementary proof of the nilpotency of Moufang loops which are of prime power order. Besides basic properties of Moufang loops and Sylow theorems, the proof relies on the fact that a relative multiplication group of a (centrally nilpotent) subloop of order pk is a p-group in any finite Moufang loop Q, and that L-1 & phi;(x)& phi;Lx & phi;-1 and R-1 & phi;(x) & phi;Rx & phi;-1 are pseudoautomorphisms of Q whenever x & ISIN; Q and & phi; is a pseudoautomorphism of Q. & COPY; 2023 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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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

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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