On the probability that a group element fixes a set and its generalized conjugacy class graph
Let G be a metacyclic 2-group. The probability that two random elements commute in G is the quotient of the number of commuting elements by the square of the order of G. This concept has been generalized and extended by several authors. One of these extensions is the probability that an element of a...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Published: |
American Institute of Physics Inc.
2015
|
| Subjects: |
| _version_ | 1796860557431668736 |
|---|---|
| author | Sarmin, Nor Haniza Omer Sanaa, Mohamed Saleh Erfanian, Ahmad |
| author_facet | Sarmin, Nor Haniza Omer Sanaa, Mohamed Saleh Erfanian, Ahmad |
| author_sort | Sarmin, Nor Haniza |
| collection | ePrints |
| description | Let G be a metacyclic 2-group. The probability that two random elements commute in G is the quotient of the number of commuting elements by the square of the order of G. This concept has been generalized and extended by several authors. One of these extensions is the probability that an element of a group fixes a set, where the set consists of all subsets of commuting elements of G of size two that are in the form (a,b), where a and b commute and lcm(|a|, |b|) = 2. In this paper, the probability that a group element fixes a set is found for metacyclic 2-groups of negative type of nilpotency class at least two. The results obtained on the size of the orbits are then applied to graph theory, more precisely to generalized conjugacy class graph. |
| first_indexed | 2024-03-05T19:43:09Z |
| format | Article |
| id | utm.eprints-58684 |
| institution | Universiti Teknologi Malaysia - ePrints |
| last_indexed | 2024-03-05T19:43:09Z |
| publishDate | 2015 |
| publisher | American Institute of Physics Inc. |
| record_format | dspace |
| spelling | utm.eprints-586842022-04-10T01:47:05Z http://eprints.utm.my/58684/ On the probability that a group element fixes a set and its generalized conjugacy class graph Sarmin, Nor Haniza Omer Sanaa, Mohamed Saleh Erfanian, Ahmad QA Mathematics Let G be a metacyclic 2-group. The probability that two random elements commute in G is the quotient of the number of commuting elements by the square of the order of G. This concept has been generalized and extended by several authors. One of these extensions is the probability that an element of a group fixes a set, where the set consists of all subsets of commuting elements of G of size two that are in the form (a,b), where a and b commute and lcm(|a|, |b|) = 2. In this paper, the probability that a group element fixes a set is found for metacyclic 2-groups of negative type of nilpotency class at least two. The results obtained on the size of the orbits are then applied to graph theory, more precisely to generalized conjugacy class graph. American Institute of Physics Inc. 2015 Article PeerReviewed Sarmin, Nor Haniza and Omer Sanaa, Mohamed Saleh and Erfanian, Ahmad (2015) On the probability that a group element fixes a set and its generalized conjugacy class graph. International Journal Of Mathematical Alysis, 9 (42008). pp. 161-167. ISSN 1312-8876 http://dx.doi.org/10.1063/1.4932489 DOI:10.1063/1.4932489 |
| spellingShingle | QA Mathematics Sarmin, Nor Haniza Omer Sanaa, Mohamed Saleh Erfanian, Ahmad On the probability that a group element fixes a set and its generalized conjugacy class graph |
| title | On the probability that a group element fixes a set and its generalized conjugacy class graph |
| title_full | On the probability that a group element fixes a set and its generalized conjugacy class graph |
| title_fullStr | On the probability that a group element fixes a set and its generalized conjugacy class graph |
| title_full_unstemmed | On the probability that a group element fixes a set and its generalized conjugacy class graph |
| title_short | On the probability that a group element fixes a set and its generalized conjugacy class graph |
| title_sort | on the probability that a group element fixes a set and its generalized conjugacy class graph |
| topic | QA Mathematics |
| work_keys_str_mv | AT sarminnorhaniza ontheprobabilitythatagroupelementfixesasetanditsgeneralizedconjugacyclassgraph AT omersanaamohamedsaleh ontheprobabilitythatagroupelementfixesasetanditsgeneralizedconjugacyclassgraph AT erfanianahmad ontheprobabilitythatagroupelementfixesasetanditsgeneralizedconjugacyclassgraph |