Abelian Extensions and Solvable Loops

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10287561" target="_blank" >RIV/00216208:11320/14:10287561 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00025-014-0382-6" target="_blank" >http://dx.doi.org/10.1007/s00025-014-0382-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00025-014-0382-6" target="_blank" >10.1007/s00025-014-0382-6</a>

Result language
angličtina
Original language name
Abelian Extensions and Solvable Loops
Original language description
Based on the recent development of commutator theory for loops, we provide both syntactic and semantic characterization of abelian normal subloops. We highlight the analogies between well known central extensions and central nilpotence on one hand, and abelian extensions and congruence solvability on the other hand. In particular, we show that a loop is congruence solvable (that is, an iterated abelian extension of commutative groups) if and only if it is not Boolean complete, reaffirming the connectionbetween computational complexity and solvability. Finally, we briefly discuss relations between nilpotence and solvability for loops and the associated multiplication groups and inner mapping groups.
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
—

Project
<a href="/en/project/GA13-01832S" target="_blank" >GA13-01832S: General algebra and its connections to computer science</a><br>
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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