A simplified proof of Moufang’s theorem

Moufang’s theorem states that if QQ is a Moufang loop with elements xx, yy and zz such that x⋅yz=xy⋅zx\cdot yz = xy \cdot z, then these three elements generate a subgroup of QQ. The paper contains a new proof of this theorem that is shorter and more transparent than the standardly used proof of Bruc...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2011-01, Vol.139 (1), p.93-98
Main Authors: DRAPAL, Ales, HALL, Jonathan I
Format: Article
Language:English
Subjects:
Ales
Exact sciences and technology
General mathematics
General, history and biography
Induction assumption
Mathematical theorems
Mathematics
Research article
Sciences and techniques of general use
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Summary:Moufang’s theorem states that if QQ is a Moufang loop with elements xx, yy and zz such that x⋅yz=xy⋅zx\cdot yz = xy \cdot z, then these three elements generate a subgroup of QQ. The paper contains a new proof of this theorem that is shorter and more transparent than the standardly used proof of Bruck.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2010-10501-4