Construction of a family of Moufang loops

Robert Curtis

Research output: Contribution to journalArticle

3 Citations (Scopus)


This paper is an excerpt from a Rayleigh essay submitted at the University of Cambridge in January 1970. We reproduce it now as it gives a general construction of a family of Moufang loops to which all bar one of the finite subloops of the Cayley algebra O belong. These subloops were classified up to isomorphism in the original essay, but are classified up to equivalence under the action of the group of symmetries of O in Boddington and Rumynin [1]. Explicitly, given a group G with an element a such that a(2) = 1 in its centre, we construct a Moufang group G in which G has index 2. G will be non-associative unless G is abelian.
Original languageEnglish
Pages (from-to)233-248
Number of pages16
JournalMathematical Proceedings of the Cambridge Philosophical Society
Publication statusPublished - 1 Mar 2007


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