The structure of commutative automorphic loops
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60460709%3A41310%2F11%3A50724" target="_blank" >RIV/60460709:41310/11:50724 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
The structure of commutative automorphic loops
Original language description
An automorphic loop (or A-loop) is a loop whose inner mapping are automorphisms. Every elemnt of a commutative A-loop generates a group, and 1/xy=1/x 1/y holds. Let Q be a finite commutative A-loop and p a prime. The loop Q has order a power of p if andonly if every element of Q has order a power of p. The loop Q decomposes as a direct product of a loop of odd order and a loop of order a power of 2. If Q is of odd order, it is solvable. If A is a subloop of Q, then |A| divides |Q|. If p divides |Q|, then Q contains an element of order p. If there is a simple nonassociative commutative A-loop, it is of exponent 2.
Czech name
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Czech description
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Classification
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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Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Transactions og the American Mathematical Society
ISSN
0002-9947
e-ISSN
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Volume of the periodical
363
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
365-384
UT code for WoS article
000282653700018
EID of the result in the Scopus database
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