The probability that an element of a metacyclic 3-group of negative type fixes a set and its orbit graph
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 consi...
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| Main Authors: | , , , |
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| Format: | Conference or Workshop Item |
| Published: |
American Institute of Physics Inc.
2016
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| Subjects: | |
| Online Access: | http://eprints.utm.my/id/eprint/73219/ https://www.scopus.com/inward/record.uri?eid=2-s2.0-84984586988&doi=10.1063%2f1.4954599&partnerID=40&md5=c8defb91500cdf5a59654795828273dd |
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| Summary: | 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. |
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