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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| Format: | Thesis |
| Language: | English |
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2010
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| Online Access: | http://eprints.usm.my/42915/ http://eprints.usm.my/42915/1/Chee_Wing_Loon24.pdf |
| _version_ | 1848879690536714240 |
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| author | Chee , Wing Loon |
| author_facet | Chee , Wing Loon |
| author_sort | Chee , Wing Loon |
| building | USM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T17:51:14Z |
| format | Thesis |
| id | usm-42915 |
| institution | Universiti Sains Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T17:51:14Z |
| publishDate | 2010 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | usm-429152019-04-12T05:26:50Z http://eprints.usm.my/42915/ Classification Of Moufang Loops Of Odd Order 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 NonPeerReviewed application/pdf en http://eprints.usm.my/42915/1/Chee_Wing_Loon24.pdf Chee , Wing Loon (2010) Classification Of Moufang Loops Of Odd Order. PhD thesis, Universiti Sains Malaysia. |
| spellingShingle | QA1 Mathematics (General) Chee , Wing Loon Classification Of Moufang Loops Of Odd Order |
| title | 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_short | Classification Of Moufang Loops
Of Odd Order
|
| title_sort | classification of moufang loops
of odd order |
| topic | QA1 Mathematics (General) |
| url | http://eprints.usm.my/42915/ http://eprints.usm.my/42915/1/Chee_Wing_Loon24.pdf |