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 SM ISO690:2012KINYON, Michael, KUNEN, Kenneth. The structure of extra loops
. In: Quasigroups and Related Systems, 2004, nr. 1(12), pp. 39-60. ISSN 1561-2848. |
| EXPORT metadate: Google Scholar Crossref CERIF DataCite Dublin Core |
| Quasigroups and Related Systems | ||||||
| Numărul 1(12) / 2004 / ISSN 1561-2848 | ||||||
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| Pag. 39-60 | ||||||
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The Sylow theorems hold for nite extra loops, as does P. Hall's theorem for nite
solvable extra loops. Every nite nonassociative extra loop Q has a nontrivial center,
Z(Q). Furthermore, Q/Z(Q) is a group whenever |Q| < 512. Loop extensions are used to
construct an in nite nonassociative extra loop with a trivial center and a nonassociative
extra loop Q of order 512 such that Q/Z(Q) is nonassociative. There are exactly 16
nonassociative extra loops of order 16p for each odd prime p.
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