A. Grishkov, Andrei V. Zavarnitsine
Abstract
Groups with triality, which arose in the papers of Glauberman and Doro, are naturally connected with Moufang loops. In this paper, we describe all possible, in a sense, groups with triality associated with a given Moufang loop. We also introduce several universal groups with triality and discuss their properties.
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Groups with triality, which arose in the papers of Glauberman and Doro, are naturally connected with Moufang loops. In this paper, we describe all possible, in a sense, groups with triality associated with a given Moufang loop. We also introduce several universal groups with triality and discuss their properties.
Key concepts: Triality, Mathematics, Pure mathematics, Group (periodic table), Algebra over a field, Physics, Quantum mechanics