Moufang loops with nonnormal commutative centre
We construct two infinite series of Moufang loops of exponent 3 whose commutative centre (i. e. the set of elements that commute with all elements of the loop) is not a normal subloop. In particular, we obtain examples of such loops of orders 38 and 311 one of which can be defined as the Moufang tri...
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| Veröffentlicht in: | Mathematical proceedings of the Cambridge Philosophical Society 2021-05, Vol.170 (3), p.609-614 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
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| Online-Zugang: | Volltext |
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| Zusammenfassung: | We construct two infinite series of Moufang loops of exponent 3 whose commutative centre (i. e. the set of elements that commute with all elements of the loop) is not a normal subloop. In particular, we obtain examples of such loops of orders 38 and 311 one of which can be defined as the Moufang triplication of the free Burnside group B(3, 3). |
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| ISSN: | 0305-0041 1469-8064 |
| DOI: | 10.1017/S0305004119000549 |