Classification Of Moufang Loops Of Odd Order
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 associativ...
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my-usm-ep.429152019-04-12T05:26:50Z Classification Of Moufang Loops Of Odd Order 2010-06 Chee , Wing Loon QA1 Mathematics (General) 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. 2010-06 Thesis http://eprints.usm.my/42915/ http://eprints.usm.my/42915/1/Chee_Wing_Loon24.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik |
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Universiti Sains Malaysia |
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USM Institutional Repository |
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English |
| topic |
QA1 Mathematics (General) |
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QA1 Mathematics (General) Chee , Wing Loon Classification Of Moufang Loops Of Odd Order |
| description |
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. |
| format |
Thesis |
| qualification_name |
Doctor of Philosophy (PhD.) |
| qualification_level |
Doctorate |
| author |
Chee , Wing Loon |
| author_facet |
Chee , Wing Loon |
| author_sort |
Chee , Wing Loon |
| title |
Classification Of Moufang Loops
Of Odd Order
|
| title_short |
Classification Of Moufang Loops
Of Odd Order
|
| title_full |
Classification Of Moufang Loops
Of Odd Order
|
| title_fullStr |
Classification Of Moufang Loops
Of Odd Order
|
| title_full_unstemmed |
Classification Of Moufang Loops
Of Odd Order
|
| title_sort |
classification of moufang loops
of odd order |
| granting_institution |
Universiti Sains Malaysia |
| granting_department |
Pusat Pengajian Sains Matematik |
| publishDate |
2010 |
| url |
http://eprints.usm.my/42915/1/Chee_Wing_Loon24.pdf |
| _version_ |
1747821126914932736 |