Classification Of Moufang Loops Of Odd Order

Chee , Wing Loon (2010) Classification Of Moufang Loops Of Odd Order. PhD thesis, Universiti Sains Malaysia.

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The Moufang identity (x · y) · (z · x) = [x · (y · z)] · x was first introduced by Ruth Moufang in 1935. Now, a loop that satisfies the Moufang identity is called a Moufang loop. Our interest is to study the question: “For a positive integer n, must every Moufang loop of order n be associative?”. If not, can we construct a nonassociative Moufang loop of order n? These questions have been studied by handling Moufang loops of even and odd order separately. For even order, Chein (1974) constructed a class of nonassociative Moufang loop, M(G, 2) of order 2m where G is a nonabelian group of order m. Following that, Chein and Rajah (2000) have proved that all Moufang loops of order 2m are associative if and only if all groups of order m are abelian.

Item Type: Thesis (PhD)
Subjects: Q Science > QA Mathematics > QA1 Mathematics (General)
Divisions: Pusat Pengajian Sains Matematik (School of Mathematical Sciences) > Thesis
Depositing User: Mr Mohammad Harish Sabri
Date Deposited: 16 Nov 2018 03:29
Last Modified: 12 Apr 2019 05:26

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