Random generators of given orders and the smallest simple Moufang loop. (Q2496155)
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scientific article
| Language | Label | Description | Also known as |
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| English | Random generators of given orders and the smallest simple Moufang loop. |
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Random generators of given orders and the smallest simple Moufang loop. (English)
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12 July 2006
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The probability that \(m\) randomly chosen elements of a finite power associative loop \(C\) generate \(C\) is calculated in terms of Hasse constants (introduced by the author just in the previous paper [ibid. 50, No. 1, 7--26 (2003; Zbl 1092.20049)]). As an illustration, all meaningful probabilities of random generation are found for the smallest non-associative simple Moufang loop.
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random generators of given orders
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Paige loops
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finite power associative loops
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subloop lattices
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simple Moufang loops
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