Classification Of Moufang Loops Of Odd Order pq3
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Date
2014-01-31
Authors
BALASINGAM GNANARAJ, ANDREW RAJAH
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
An open problem in the theory of Moufang loops is to classify those loops which are minimally non associative, that is,
loops which are non associative but where all proper subloops are associative. A related question is to classify all
integers n for which a minimally nonassociative Moufang loop exists. In [Possible orders of nonassociative Moufang
loops, Comment. Math. Univ. Carolin. 41~2) (2000) 237-244], O. Chein and A. Rajah showed that a minimal
non associative Moufang loop of order 2q can be constructed by using a non-abelian group of order q3. In [Moufang
loops of odd order pq3, J. Algebra 235 (2001) 66-93], A. Rajah proved that for odd primes p < q, a nonassociative
Moufang loops of order pq3 exists if and only if q:: 1 (mod p). We have completely classified all minimally
nonassociative Moufang loops of order pq3 for primes p < q. This result has been published as a joint article with Wing
Loon Chee and Stephen M. Gagola III titled "Classification of minimal non associative Moufang loops of order pq311 in
International Journal of Algebra and Computation, Volume 23, NO.8 (2013) 1895-1908 on 22 January 2014.