COPRIME DEGREE OF SOME GROUPS AND ITS RELATION TO COPRIME GRAPHS
Coprime degree of a group can be seen as a generalization of commutativity degree of a group. Coprime degree of a group is defined to be the probability that two random elements in the group have coprime orders. Meanwhile, the coprime graph of a finite group is a graph where the set of vertices i...
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id-itb.:734102023-06-20T09:47:55ZCOPRIME DEGREE OF SOME GROUPS AND ITS RELATION TO COPRIME GRAPHS Gazir S, Abdul Indonesia Theses coprime degree, coprime graph, cyclic groups, dihedral groups, generalized quaternion groups. INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/73410 Coprime degree of a group can be seen as a generalization of commutativity degree of a group. Coprime degree of a group is defined to be the probability that two random elements in the group have coprime orders. Meanwhile, the coprime graph of a finite group is a graph where the set of vertices is a elements of a group, and two distinct vertices are adjacent if their order is coprime. In this paper, we derive explicit description of coprime degree for several finite groups with respect to the prime decompositions of their group orders, including cyclic groups, dihedral groups, and generalized quaternion groups. Furthermore, we establish the relation between coprime degree of a group and its coprime graph text |
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| description |
Coprime degree of a group can be seen as a generalization of commutativity degree
of a group. Coprime degree of a group is defined to be the probability that two
random elements in the group have coprime orders. Meanwhile, the coprime graph
of a finite group is a graph where the set of vertices is a elements of a group, and
two distinct vertices are adjacent if their order is coprime. In this paper, we derive
explicit description of coprime degree for several finite groups with respect to
the prime decompositions of their group orders, including cyclic groups, dihedral
groups, and generalized quaternion groups. Furthermore, we establish the relation
between coprime degree of a group and its coprime graph |
| format |
Theses |
| author |
Gazir S, Abdul |
| spellingShingle |
Gazir S, Abdul COPRIME DEGREE OF SOME GROUPS AND ITS RELATION TO COPRIME GRAPHS |
| author_facet |
Gazir S, Abdul |
| author_sort |
Gazir S, Abdul |
| title |
COPRIME DEGREE OF SOME GROUPS AND ITS RELATION TO COPRIME GRAPHS |
| title_short |
COPRIME DEGREE OF SOME GROUPS AND ITS RELATION TO COPRIME GRAPHS |
| title_full |
COPRIME DEGREE OF SOME GROUPS AND ITS RELATION TO COPRIME GRAPHS |
| title_fullStr |
COPRIME DEGREE OF SOME GROUPS AND ITS RELATION TO COPRIME GRAPHS |
| title_full_unstemmed |
COPRIME DEGREE OF SOME GROUPS AND ITS RELATION TO COPRIME GRAPHS |
| title_sort |
coprime degree of some groups and its relation to coprime graphs |
| url |
https://digilib.itb.ac.id/gdl/view/73410 |
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1822993021372727296 |