TY - JOUR

T1 - Construction of a family of Moufang loops

AU - Curtis, Robert

PY - 2007/3/1

Y1 - 2007/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34247874543&partnerID=8YFLogxK

U2 - 10.1017/S0305004106009789

DO - 10.1017/S0305004106009789

M3 - Article

SN - 0305-0041

VL - 142

SP - 233

EP - 248

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

ER -