Conjugacy classes and graphs of twogroups of nilpotency class two
Two elements a and b of a group are called conjugate if there exists an element g in the group such that gag??1 = b: The set of all conjugates in a group forms the conjugacy classes of the group. The main objective of this research is to determine the number and size of conjugacy classes for 2gener...
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myutmep.4396620170622T02:28:43Z Conjugacy classes and graphs of twogroups of nilpotency class two 201309 Ilangovan, Sheila QA Mathematics Two elements a and b of a group are called conjugate if there exists an element g in the group such that gag??1 = b: The set of all conjugates in a group forms the conjugacy classes of the group. The main objective of this research is to determine the number and size of conjugacy classes for 2generator 2groups of nilpotency class two. Suppose G is a 2generator 2group of class two which comprises of three types, namely Type 1, Type 2 and Type 3. The general formulas for the number of conjugacy classes of G are determined by using the base group and central extension method, respectively. It is found that for each type of the group G, the number of conjugacy classes consists of two general formulas. Moreover, the conjugacy class sizes are computed based on the order of the derived subgroup. The results are then applied into graph theory. The conjugacy class graph of G is proven as a complete graph. Consequently, some properties of the graph related to conjugacy classes of the group are found. This includes the number of connected components, diameter, the number of edges and the regularity of the graph. Furthermore, the clique number and chromatic number for groups of Type 1, 2 and 3 are shown to be identical. Besides, some properties of the graph related to commuting conjugacy classes of abelian and dihedral groups are introduced. 201309 Thesis http://eprints.utm.my/id/eprint/43966/ http://eprints.utm.my/id/eprint/43966/5/SheilaIlangovanPFS2013.pdf application/pdf en public phd doctoral Universiti Teknologi Malaysia, Faculty of Science Faculty of Science 
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UTM Institutional Repository 
language 
English 
topic 
QA Mathematics 
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QA Mathematics Ilangovan, Sheila Conjugacy classes and graphs of twogroups of nilpotency class two 
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Two elements a and b of a group are called conjugate if there exists an element g in the group such that gag??1 = b: The set of all conjugates in a group forms the conjugacy classes of the group. The main objective of this research is to determine the number and size of conjugacy classes for 2generator 2groups of nilpotency class two. Suppose G is a 2generator 2group of class two which comprises of three types, namely Type 1, Type 2 and Type 3. The general formulas for the number of conjugacy classes of G are determined by using the base group and central extension method, respectively. It is found that for each type of the group G, the number of conjugacy classes consists of two general formulas. Moreover, the conjugacy class sizes are computed based on the order of the derived subgroup. The results are then applied into graph theory. The conjugacy class graph of G is proven as a complete graph. Consequently, some properties of the graph related to conjugacy classes of the group are found. This includes the number of connected components, diameter, the number of edges and the regularity of the graph. Furthermore, the clique number and chromatic number for groups of Type 1, 2 and 3 are shown to be identical. Besides, some properties of the graph related to commuting conjugacy classes of abelian and dihedral groups are introduced. 
format 
Thesis 
qualification_name 
Doctor of Philosophy (PhD.) 
qualification_level 
Doctorate 
author 
Ilangovan, Sheila 
author_facet 
Ilangovan, Sheila 
author_sort 
Ilangovan, Sheila 
title 
Conjugacy classes and graphs of twogroups of nilpotency class two 
title_short 
Conjugacy classes and graphs of twogroups of nilpotency class two 
title_full 
Conjugacy classes and graphs of twogroups of nilpotency class two 
title_fullStr 
Conjugacy classes and graphs of twogroups of nilpotency class two 
title_full_unstemmed 
Conjugacy classes and graphs of twogroups of nilpotency class two 
title_sort 
conjugacy classes and graphs of twogroups of nilpotency class two 
granting_institution 
Universiti Teknologi Malaysia, Faculty of Science 
granting_department 
Faculty of Science 
publishDate 
2013 
url 
http://eprints.utm.my/id/eprint/43966/5/SheilaIlangovanPFS2013.pdf 
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1747817124904042496 