Every Moufang loop of odd order with nontrivial commutant has nontrivial center |
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Authors: | Piroska Csörgő |
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Institution: | 1. Department of Algebra and Number Theory, E?tv?s University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary
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Abstract: | We get a partial result for Phillips’ problem: does there exist a Moufang loop of odd order with trivial nucleus? First we show that a Moufang loop Q of odd order with nontrivial commutant has nontrivial nucleus, then, by using this result, we prove that the existence of a nontrivial commutant implies the existence of a nontrivial center in Q. Introducing the notion of commutantly nilpotence, we get that the commutantly nilpotence is equivalent to the centrally nilpotence for the Moufang loops of odd order. |
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