Generators of nonassociative simple Moufang loops over finite prime fields (Q5946414)
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scientific article; zbMATH DE number 1658812
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generators of nonassociative simple Moufang loops over finite prime fields |
scientific article; zbMATH DE number 1658812 |
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Generators of nonassociative simple Moufang loops over finite prime fields (English)
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12 August 2002
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octonions
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generators
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finite simple Moufang loops
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nonassociative simple Moufang loops
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integral Cayley numbers
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0.8954805
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0.86057615
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0.85969406
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0.8566389
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0.85172105
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0.84943485
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0.84815854
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A finite simple Moufang loop is either associative or nonassociative. It is known that the nonassociative Moufang loops cannot be generated by two elements only. The author proves that the nonassociative simple Moufang loops (NSML) over finite prime fields are generated by three elements.NEWLINENEWLINENEWLINEThe smallest NSML of 120 elements is isomorphic to the integral Cayley numbers of unit norm modulo their center [\textit{L. J. Paige}, Proc. Am. Math. Soc. 7, 471-482 (1956; Zbl 0070.25302)]. In this paper there is given an explicit isomorphism and shown that the loop of integral Cayley numbers of unit norm is generated multiplicatively by three elements.
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