The exact number and size of conjugacy classes, commutativity degrees and non-commuting graphs of finite metacyclic groups
Also available in printed version : QA174.2 K39 2013 raf
| 第一著者: | |
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| その他の著者: | |
| フォーマット: | Doctoral thesis |
| 出版事項: |
Universiti Teknologi Malaysia
2025
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| 主題: | |
| オンライン･アクセス: | https://utmik.utm.my/handle/123456789/101590 |
| Abstract | Abstract here |
| _version_ | 1854975040805666816 |
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| author | Kayvan Moradipour |
| author2 | Nor Haniza Sarmin, supervisor |
| author_facet | Nor Haniza Sarmin, supervisor Kayvan Moradipour |
| author_sort | Kayvan Moradipour |
| description | Also available in printed version : QA174.2 K39 2013 raf |
| format | Doctoral thesis |
| id | utm-123456789-101590 |
| institution | Universiti Teknologi Malaysia |
| publishDate | 2025 |
| publisher | Universiti Teknologi Malaysia |
| record_format | dspace |
| record_pdf | Abstract |
| spelling | utm-123456789-1015902025-08-20T15:55:57Z The exact number and size of conjugacy classes, commutativity degrees and non-commuting graphs of finite metacyclic groups Kayvan Moradipour Nor Haniza Sarmin, supervisor Conjugacy classes Also available in printed version : QA174.2 K39 2013 raf The objectives of the research are to obtain the exact number and size of conjugacy classes, commutativity and n-th commutativity degrees of non-abelian metacyclic p-groups, and to investigate some non-commuting graph theoretical properties of metacyclic p-groups. The classification of metacyclic p-groups, denoted as G, was divided into three types which are denoted as Type I, Type II and Type III. The center, the order of the center, and the correspondence between the conjugacy classes of the central factor group of G and conjugacy classes of G were used for computing the number of the respective conjugacy classes. The commutativity degree of G was determined by dividing the number of conjugacy classes of G by the order of G. The size of conjugacy classes and n-th commutativity degree of G was computed using centralizer and order of the centralizer of G: The degree of vertices and the number of edges in the non-commuting graph of G; the center and the centralizer of G were also used to investigate the relationship between the graph-theoretic properties and the algebraic properties of G. For each type of metacyclic p-groups, general formulas for the exact number and size of conjugacy classes and n-th commutativity degree in terms of their parameters were derived. Furthermore, necessary and sufficient conditions under which two metacyclic p-groups have isomorphic noncommuting graphs were given. This research illustrates that the number of conjugacy classes of G and its respective size, and the n-th commutativity for non-isomorphic metacyclic p-groups of each type were found to be the same. Moreover, two metacyclic p-groups which have isomorphic graphs were found to have the same order and center atiff UTM 120 p. Thesis (Ph.D (Matematik)) - Universiti Teknologi Malaysia, 2013 2025-04-10T04:49:36Z 2025-04-10T04:49:36Z 2013 Doctoral thesis https://utmik.utm.my/handle/123456789/101590 valet-20160131-112126 vital:83830 Closed Access UTM Complete Unpublished application/pdf Universiti Teknologi Malaysia |
| spellingShingle | Conjugacy classes Kayvan Moradipour The exact number and size of conjugacy classes, commutativity degrees and non-commuting graphs of finite metacyclic groups |
| thesis_level | PhD |
| title | The exact number and size of conjugacy classes, commutativity degrees and non-commuting graphs of finite metacyclic groups |
| title_full | The exact number and size of conjugacy classes, commutativity degrees and non-commuting graphs of finite metacyclic groups |
| title_fullStr | The exact number and size of conjugacy classes, commutativity degrees and non-commuting graphs of finite metacyclic groups |
| title_full_unstemmed | The exact number and size of conjugacy classes, commutativity degrees and non-commuting graphs of finite metacyclic groups |
| title_short | The exact number and size of conjugacy classes, commutativity degrees and non-commuting graphs of finite metacyclic groups |
| title_sort | exact number and size of conjugacy classes commutativity degrees and non commuting graphs of finite metacyclic groups |
| topic | Conjugacy classes |
| url | https://utmik.utm.my/handle/123456789/101590 |
| work_keys_str_mv | AT kayvanmoradipour theexactnumberandsizeofconjugacyclassescommutativitydegreesandnoncommutinggraphsoffinitemetacyclicgroups AT kayvanmoradipour exactnumberandsizeofconjugacyclassescommutativitydegreesandnoncommutinggraphsoffinitemetacyclicgroups |