Product of Conjugacy Classes of the Alternating Group An
For a nonempty subset X of a group G and a positive integer m , the product of X , denoted by Xm ,is the set Xm = That is , Xm is the subset of G formed by considering all possible ordered products of m elements form X. In the symmetric g...
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University of Baghdad, College of Science for Women
2012-09-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/1398 |
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| author | Baghdad Science Journal |
| author_facet | Baghdad Science Journal |
| author_sort | Baghdad Science Journal |
| collection | DOAJ |
| description | For a nonempty subset X of a group G and a positive integer m , the product of X , denoted by Xm ,is the set
Xm =
That is , Xm is the subset of G formed by considering all possible ordered products of m elements form X. In the symmetric group Sn, the class Cn (n odd positive integer) split into two conjugacy classes in An denoted Cn+ and Cn- . C+ and C- were used for these two parts of Cn. This work we prove that for some odd n ,the class C of 5- cycle in Sn has the property that = An n 7 and C+ has the property that each element of C+ is conjugate to its inverse, the square of each element of it is the element of C-, these results were used to prove that C+ C- = An exceptional of I (I the identity conjugacy class), when n=5+4k , k>=0. |
| format | Article |
| id | doaj-art-fd3a6b7ccb554de187b43deab9f456f2 |
| institution | Kabale University |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2012-09-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-fd3a6b7ccb554de187b43deab9f456f22025-08-20T03:58:03ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862012-09-019310.21123/bsj.9.3.565-568Product of Conjugacy Classes of the Alternating Group AnBaghdad Science JournalFor a nonempty subset X of a group G and a positive integer m , the product of X , denoted by Xm ,is the set Xm = That is , Xm is the subset of G formed by considering all possible ordered products of m elements form X. In the symmetric group Sn, the class Cn (n odd positive integer) split into two conjugacy classes in An denoted Cn+ and Cn- . C+ and C- were used for these two parts of Cn. This work we prove that for some odd n ,the class C of 5- cycle in Sn has the property that = An n 7 and C+ has the property that each element of C+ is conjugate to its inverse, the square of each element of it is the element of C-, these results were used to prove that C+ C- = An exceptional of I (I the identity conjugacy class), when n=5+4k , k>=0.http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/1398" conjugacy classes ,split, Alternating Group, Product" |
| spellingShingle | Baghdad Science Journal Product of Conjugacy Classes of the Alternating Group An مجلة بغداد للعلوم " conjugacy classes ,split, Alternating Group, Product" |
| title | Product of Conjugacy Classes of the Alternating Group An |
| title_full | Product of Conjugacy Classes of the Alternating Group An |
| title_fullStr | Product of Conjugacy Classes of the Alternating Group An |
| title_full_unstemmed | Product of Conjugacy Classes of the Alternating Group An |
| title_short | Product of Conjugacy Classes of the Alternating Group An |
| title_sort | product of conjugacy classes of the alternating group an |
| topic | " conjugacy classes ,split, Alternating Group, Product" |
| url | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/1398 |
| work_keys_str_mv | AT baghdadsciencejournal productofconjugacyclassesofthealternatinggroupan |