On half-automorphisms of certain Moufang loops with even order

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10188761" target="_blank" >RIV/00216208:11320/13:10188761 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jalgebra.2013.03.026" target="_blank" >http://dx.doi.org/10.1016/j.jalgebra.2013.03.026</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jalgebra.2013.03.026" target="_blank" >10.1016/j.jalgebra.2013.03.026</a>

Result language
angličtina
Original language name
On half-automorphisms of certain Moufang loops with even order
Original language description
A half-isomorphism phi :G -> K between multiplicative systems G and K is a bijection from G onto K such that phi(ab) is an element of {phi(a)phi(b), phi(b)phi(a)} for any a,b is an element of G. It was shown by Scott (1957) [8] that if G is a group thenphi is either an isomorphism or an anti-isomorphism. This, along with Frobenius' original papers on character theory, was used to prove that a finite group is determined by its group determinant. It was then shown by Gagola and Giuliani (2012) [5] that Scott's result carries over to Moufang loops of odd order. However, such a result does not hold for all Moufang loops that are of even order. Here we look at certain Moufang loops of even order and determine under what conditions is a half-automorphism forced to be either an automorphism or an anti-automorphism.
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
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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