On the nuclei of Moufang loops with orders coprime to six

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On the nuclei of Moufang loops with orders coprime to six

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the nuclei of Moufang loops with orders coprime to six

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Algebra

ISSN

0021-8693

e-ISSN

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Svazek periodika

2014

Číslo periodika v rámci svazku

402

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

280-293

Kód UT WoS článku

000331418500011

EID výsledku v databázi Scopus

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