Commutator theory for loops

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10287308" target="_blank" >RIV/00216208:11320/14:10287308 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jalgebra.2013.08.045" target="_blank" >http://dx.doi.org/10.1016/j.jalgebra.2013.08.045</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jalgebra.2013.08.045" target="_blank" >10.1016/j.jalgebra.2013.08.045</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Commutator theory for loops

Popis výsledku v původním jazyce

Using the Freese-McKenzie commutator theory for congruence modular varieties as the starting point, we develop commutator theory for the variety of loops. The fundamental theorem of congruence commutators for loops relates generators of the congruence commutator to generators of the total inner mapping group. We specialize the fundamental theorem into several varieties of loops, and also discuss the commutator of two normal subloops. Consequently, we argue that some standard definitions of loop theory,such as elementwise commutators and associators, should be revised and linked more closely to inner mappings. Using the new definitions, we prove several natural properties of loops that could not be so elegantly stated with the standard definitions of loop theory. For instance, we show that the subloop generated by the new associators defined here is automatically normal. We conclude with a preliminary discussion of abelianess and solvability in loops. (C) 2013 Elsevier Inc. All rights

Název v anglickém jazyce

Commutator theory for loops

Popis výsledku anglicky

Using the Freese-McKenzie commutator theory for congruence modular varieties as the starting point, we develop commutator theory for the variety of loops. The fundamental theorem of congruence commutators for loops relates generators of the congruence commutator to generators of the total inner mapping group. We specialize the fundamental theorem into several varieties of loops, and also discuss the commutator of two normal subloops. Consequently, we argue that some standard definitions of loop theory,such as elementwise commutators and associators, should be revised and linked more closely to inner mappings. Using the new definitions, we prove several natural properties of loops that could not be so elegantly stated with the standard definitions of loop theory. For instance, we show that the subloop generated by the new associators defined here is automatically normal. We conclude with a preliminary discussion of abelianess and solvability in loops. (C) 2013 Elsevier Inc. All rights

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

—

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

399

Číslo periodika v rámci svazku

399

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

33

Strana od-do

290-322

Kód UT WoS článku

000330006200016

EID výsledku v databázi Scopus

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