On the probability that an element of metacyclic 2-group of positive type fixes a set and its generalized conjugacy class graph
The probability that an element of a group fixes a set is considered as one of the extensions of commutativity degree that can be obtained by some group actions on a set. We denote G as a metacyclic 2-group of positive type of nilpotency of class at least three and O as the set of all subsets of all...
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| Main Authors: | , |
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| Format: | Article |
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Research India Publications
2015
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| Online Access: | http://eprints.utm.my/id/eprint/58685/ https://www.ripublication.com/Volume/ijaerv10n15.htm |
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| Summary: | The probability that an element of a group fixes a set is considered as one of the extensions of commutativity degree that can be obtained by some group actions on a set. We denote G as a metacyclic 2-group of positive type of nilpotency of class at least three and O as the set of all subsets of all commuting elements of G of size two in the form of a,b , where a and b commute and each of order two. In this paper, we compute the probability that an element of G fixes a set in which G acts regularly on O. Then the results are applied to graph theory, more precisely to generalized conjugacy class graph. |
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