Zamri, S. N. A. and Sarmin, N. H. and Omer, S. M. S. and El-Sanfaz, M. A.
(2016)
*The probability that an element of a metacyclic 3-group of negative type fixes a set and its orbit graph.*
In: 23rd Malaysian National Symposium of Mathematical Sciences: Advances in Industrial and Applied Mathematics, SKSM 2015, 24 November 2015 through 26 November 2015, Johor Bahru; Malaysia.

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## Abstract

In this paper, let G be a metacyclic 3-group of negative type of nilpotency class at least three. Let ω be the set of all subsets of commuting elements of G of size three in the form of (a,b), where a and b commute and lcm a , b 3 . The probability that an element of a group G fixes a set ω is considered as one of the extensions of the commutativity degree that can be obtained under group actions on a set. In this paper, we compute the probability that an element of G fixes a set ωin which G acts on ωby conjugation. The results are then applied to graph theory, more precisely to orbit graph.

Item Type: | Conference or Workshop Item (Paper) |
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Uncontrolled Keywords: | nilpotency class |

Subjects: | Q Science > QA Mathematics |

Divisions: | Science |

ID Code: | 73219 |

Deposited By: | Muhammad Atiff Mahussain |

Deposited On: | 28 Nov 2017 15:42 |

Last Modified: | 28 Nov 2017 15:42 |

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