On the nuclei of Moufang loops with orders coprime to six

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10287261" target="_blank" >RIV/00216208:11320/14:10287261 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jalgebra.2013.10.033" target="_blank" >http://dx.doi.org/10.1016/j.jalgebra.2013.10.033</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jalgebra.2013.10.033" target="_blank" >10.1016/j.jalgebra.2013.10.033</a>

Result language
angličtina
Original language name
On the nuclei of Moufang loops with orders coprime to six
Original language description
An open problem, originally proposed by J.D. Phillips, asks if there exists an odd ordered Moufang loop that possesses a trivial nucleus. In 1968 George Glauberman proved [7] that if Q is a Moufang loop of odd order and M is any minimal normal subloop ofQ whose order is coprime to its index in Q, then M is contained in the nucleus of Q. We are able to strengthen Glauberman's result here by removing the coprime assumption between the order of M and its index in Q given that the loop Q has an order not divisible by three (in addition to being of odd order). Thus, a nontrivial Moufang loop having an order coprime to six certainly has a nontrivial nucleus. Concerning then the question raised by J.D. Phillips, any nontrivial Moufang loop of odd order witha trivial nucleus (should one exist) must have an order divisible by three. (C) 2013 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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