About the embedding of Moufang loops in alternative algebras II
| Autor: | Sandu, N. I. |
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| Rok vydání: | 2008 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | It is known that with precision till isomorphism that only and only loops $M(F) = M_0(F)/<-1>$, where $M_0(F)$ denotes the loop, consisting from elements of all matrix Cayley-Dickson algebra $C(F)$ with norm 1, and $F$ be a subfield of arbitrary fixed algebraically closed field, are simple non-associative Moufang loops. In this paper it is proved that the simple loops $M(F)$ they and only they are not embedded into a loops of invertible elements of any unitaly alternative algebras if $\text{char} F \neq 2$ and $F$ is closed under square root operation. For the remaining Moufang loops such an embedding is possible. Using this embedding it is quite simple to prove the well-known finding: the finite Moufang $p$-loop is centrally nilpotent. Comment: 15 pages |
| Databáze: | arXiv |
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